# an estimator is said to be consistent if:

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An estimator is consistent if it satisfies two conditions: a. 4.5K views 56.34 C. 62.96 d. 66.15 5. Consistency as defined here is sometimes referred to as weak consistency. This notion â¦ "Converges" can be interpreted various ways with random sequences, so you get different kinds of consistency depending on the type of convergence. c. Population has any distribution and n is any size d. All of these choices allow you to use the formula 12. Select the best response 1. If this is the case, then we say that our statistic is an unbiased estimator of the parameter. The width of a confidence interval estimate of the population mean increases when the a. level of confidence increases b. sample size decreases c. value of the population standard deviation increases d. All of these choices are true. "XT- a. Let {âTn(XÎ¸)â} be a sequence of estimators for soâ¦ Privacy We want our estimator to match our parameter, in the long run. If the confidence level is reduced, the confidence interval: The letter a(alpha) in the formula for constructing a confidence interval estimate of the population proportion is: The width of a confidence interval estimate of the population mean increases when the: After constructing a confidence interval estimate for a population proportion, you believe that the interval is useless because it is too wide. 95% C. 99% d. None of these choices, statistics and probability questions and answers. In statistics, the bias of an estimator is the difference between this estimator's expected value and the true value of the parameter being estimated. An estimator of a given parameter is said to be unbiased if its expected value is equal to the true value of the parameter.. The sample size needed to estimate a population mean to within 50 units was found to be 97. We can thus define an absolute efficiency of an estimator as the ratio between the minimum variance and the actual variance. Unbiased estimators whose variance approaches Î¸ as n â â are consistent. an unbiased estimator is said to be consistent if the difference between the estimator and the parameter grows smaller as the sample size grows larger. In general, if $\hat{\Theta}$ is a point estimator for $\theta$, we can write 0.025 c. 1.65 d. 1.96 9. If there are two unbiased estimators of a population parameter available, the one that has the smallest variance is said to be: 50.92 12.14 C. 101.84 t 4.28 d. 50.921 4.28 7. This occurs frequently in estimation of scale parameters by measures of statistical dispersion. An estimator is said to be consistent if: the difference between the estimator and the population parameter grows smaller as the sample size grows larger. a. In order to correct this problem, you need to a. increase the sample size b. increase the population standard deviation. d. None of these choices C. The confidence level d. The value of the population mean. variance). We now define unbiased and biased estimators. This simply means that, for an estimator to be consistent it must have both a small bias and small variance. View desktop site. explanation................................................. 1.An estimator is said to be consistent if: the difference between the estimator and the population parameter grows smaller as the sample size grows larger. For the validity of OLS estimates, there are assumptions made while running linear regression models.A1. 11. which of the following conditions does not allow you to use the formula x Â± to estimate u? A point estimate of the population mean. lim n â â E (Î± ^) = Î±. © 2003-2020 Chegg Inc. All rights reserved. Suppose {pÎ¸: Î¸âââÎ} is a family of distributions (the parametric model), and XÎ¸ = {X1, X2, â¦ : Xi ~ pÎ¸} is an infinite sample from the distribution pÎ¸. Consistent Estimator An estimator Î± ^ is said to be a consistent estimator of the parameter Î± ^ if it holds the following conditions: Î± ^ is an unbiased estimator of Î±, so if Î± ^ is biased, it should be unbiased for large values of n (in the limit sense), i.e. Unbiased and Biased Estimators . An Estimator Is Said To Be Consistent If A. An unbiased estimator of a population parameter is defined as: an estimator whose expected value is equal to the parameter. An estimator is consistent if it converges to the right thing as the sample size tends to infinity. | If convergence is almost certain then the estimator is said to be strongly consistent (as the sample size reaches infinity, the probability of the estimator being equal to the true value becomes 1). Consistency in the statistical sense isnât about how consistent the dart-throwing is (which is actually âprecisionâ, i.e. An unbiased estimator of a population parameter is defined as a. an estimator whose expected value is equal to the parameter b. an estimator whose variance is equal to one c. an estimator whose expected value is equal to zero d. an estimator whose variance goes to zero as the sample size goes to infinity 3. The larger the confidence level, the a. smaller the value of za/ 2. b. wider the confidence interval. d. the level of consistency 4. by Marco Taboga, PhD. Consistency. 6.62 b. They work better when the estimator do not have a variance. Loosely speaking, an estimator Tn of parameter Î¸ is said to be consistent, if it converges in probability to the true value of the parameter: A more rigorous definition takes into account the fact that Î¸ is actually unknown, and thus the convergence in probability must take place for every possible value of this parameter. b. Deï¬nition 7.2.1 (i) An estimator Ëa n is said to be almost surely consistent estimator of a 0,ifthereexistsasetM â Î©,whereP(M)=1and for all Ï â M we have Ëa n(Ï) â a. c. smaller the probability that the confidence interval will contain the population mean. Consistency An estimator is said to be consistent if the statistic to be used as estimator becomes closer and closer to the population parameter being estimator as the sample size n increases. If there are two unbiased estimators of a parameter, the one whose variance is smaller is said to be relatively efficient. Population is normally distributed and the population variance is known. An unbiased estimator is said to be consistent if the difference between the estimator and the parameter grows smaller as the sample size grows larger. Inconsistent just means not consistent. If the population standard deviation was 50, then the confidence level used was: a. The estimates which are obtained should be unbiased and consistent to represent the true value of the population. In developing an interval estimate for a population mean, the population standard deviation Ï was assumed to be 10. Its variance converges to 0 as the sample size increases. That is, Î¸ ^ is consistent if, as the sample size gets larger, it is less and less likely that Î¸ ^ will be further than â from the true value of Î¸. Consistency is related to bias ; see bias versus consistency . Information and translations of consistent estimator in the most comprehensive dictionary definitions resource on the web. The term 1 - a refers to: a. the probability that a confidence interval does not contain the population parameter b. the confidence level C. the level of unbiasedness. In other words, an estimator is unbiased if it produces parameter estimates that are on average correct. Point estimation is the opposite of interval estimation. To check consistency of the estimator, we consider the following: ï¬rst, we consider data simulated from the GP density with parameters ( 1 , Î¾ 1 ) and ( 3 , Î¾ 2 ) for the scale and shape respectively before and after the change point. An estimator is said to be consistent if a. the difference between the estimator and the population parameter grows smaller as the sample b. C. d. size grows larger it is an unbiased estimator the variance of the estimator is zero. If the population standard deviation was 250, then the confidence level used was a. Sampling If an estimator, say Î¸, approaches the parameter Î¸ closer and closer as the sample size n increases, Î¸ is said to be a consistent estimator of Î¸. The sample size needed to estimate a population mean within 2 units with a 95% confidence when the population standard deviation equals 8 is a. This means that the distributions of the estimates become more and more concentrated near the true value of the parameter being estimated, so that the probability of the estimator being arbitrarily close to Î¸0 convergeâ¦ As the number of random variables increase, the degree of concentration should be higher and higher around the estimate in order to make the estimator of estimation the consistent estimator. The zal value for a 95% confidence interval estimate for a population mean Î¼ is a. 6. 13. Linear regression models have several applications in real life. Which of the following is not a part of the formula for constructing a confidence interval estimate of the population mean? Which of the following is not a part of the formula for constructing a confidence interval estimate of the population proportion? Guy Lebanon May 1, 2006 It is satisfactory to know that an estimator Î¸Ëwill perform better and better as we obtain more examples. Unbiased estimators An estimator Î¸Ë= t(x) is said to be unbiased for a function ... Fisher consistency An estimator is Fisher consistent if the estimator is the same functional of the empirical distribution function as the parameter of the true distribution function: Î¸Ë= h(F The sample size needed to estimate a population mean to within 10 units was found to be 68. To estimate the mean of a normal population whose standard deviation is 6, with a bound on the error of estimation equal to 1.2 and confidence level 99% requires a sample size of at least a 166 b. Estimators with this property are said to be consistent. An estimator is said to be consistent if a. the difference between the estimator and the population parameter grows smaller as the sample b. C. d. size grows larger it is an unbiased estimator the variance of the estimator is zero. The STANDS4 Network ... it is called a consistent estimator; otherwise the estimator is said to be inconsistent. If the confidence level is reduced, the confidence interval a. widens. & It is directly proportional to the square of the maximum allowable error B. Unbiased estimator. 90% b. 8. Multiple Choice. Remark: To be speciï¬c we may call this âMSE-consistantâ. An estimator is said to be consistent if, Multiple Choice. Also an estimator is said to be consistent if the variance of the estimator tends to zero as . When estimating the population proportion and the value of p is unknown, we can construct a confidence interval using which of the following? For example, as N tends to infinity, V(Î¸Ë X) = Ï5/N = 0. 6. Remember that the best or most efficient estimator of a population parameter is one which give the smallest possible variance. An estimator that converges to a multiple of a parameter can be made into a consistent estimator by multiplying the estimator by a scale factor, namely the true value divided by the asymptotic value of the estimator. n(1/n) = 0, ¯x is a consistent estimator of Î¸. In order to correct this problem, you need to: a lower and upper confidence limit associated with a specific level of confidence. 90% d. None of these choices 16. 95% Ð¡. c. narrows. Consistent estimator A consistent estimator is the one that gives the true value of the population parameter when the size of the population increases. b. 61 d. None of these choices 15. Please give An estimator is said to be consistent if its value approaches the actual, true parameter (population) value as the sample size increases. An estimator Î¸ is said to be consistent if for any â > 0, P ( | Î¸ ^ - Î¸ | â¥ â ) â 0 as n â â . Which of the following statements is false regarding the sample size needed to estimate a population proportion? The population standard deviation was assumed to be 6.50, and a sample of 100 observations was used. 2.A point estimator is defined as: b.a single value that estimates an unknown population parameter. When we replace convergence in probability with almost sure convergence, then the estimator is said to be strongly consistent. (ii) An estimator aË n is said to converge in probability to a 0, if for every Î´>0 P(|Ëa n âa| >Î´) â 0 T ââ. Formally,anunbiasedestimator Ëµforparameterµis said to be consistent if V(Ëµ) approaches zero as n â â. Suppose an interval estimate for the population mean was 62.84 to 69.46. In econometrics, Ordinary Least Squares (OLS) method is widely used to estimate the parameters of a linear regression model. An estimator is said to be consistent if: the difference between the estimator and the population parameter grows smaller as the sample size grows larger. a single value that estimates an unknown population parameter. It uses sample data when calculating a single statistic that will be the best estimate of the unknown parameter of the population. C. increase the level of confidence d. increase the sample mean 10. The conditional mean should be zero.A4. When we have no information as to the value of p, p=.50 is used because, the value of p(1-p)is at its maximum value at p=.50, If everything is held equal, and the margin of error is increased, then the sample size will. In statistics, a consistent estimator or asymptotically consistent estimator is an estimatorâa rule for computing estimates of a parameter Î¸0âhaving the property that as the number of data points used increases indefinitely, the resulting sequence of estimates converges in probabilityto Î¸0. In estimation, the estimators that give consistent estimates are said to be the consistent estimators. An estimator is said to be consistent if the difference between the estimator and the population parameter grows smaller as the sample size grows larger. d. disappears. A point estimator is a statistic used to estimate the value of an unknown parameter of a population. The problem with relying on a point estimate of a population parameter is that: the probability that a confidence interval does contain the population parameter. Select The Best Response 1. If this sequence converges in probability to the true value Î¸0, we call it a consistent estimator; otherwise the estimator is said to be inconsistent. If there are two unbiased estimators of a population parameter available, the one that has the smallest variance is said to be: Which of the following statements is correct? The sample proportion is an unbiased estimator of the population proportion. b. remains the same. 0.95 b. Which of the following is not a characteristic for a good estimator? 60.92 t 2.14 b. the difference between the estimator and the population parameter stays the same as the sample size grows larger 2. 4. The consistency as defined here is sometimes referred to as the weak consistency. 99% b. After constructing a confidence interval estimate for a population mean, you believe that the interval is useless because it is too wide. The two main types of estimators in statistics are point estimators and interval estimators. Terms From the above example, we conclude that although both $\hat{\Theta}_1$ and $\hat{\Theta}_2$ are unbiased estimators of the mean, $\hat{\Theta}_2=\overline{X}$ is probably a better estimator since it has a smaller MSE. the difference between the estimator and the population parameter stays the same as the sample size grows larger 2. An unbiased estimator is said to be consistent if the diï¬erence between the estimator and the target popula- tionparameterbecomessmallerasweincreasethesample size. If at the limit n â â the estimator tend to be always right (or at least arbitrarily close to the target), it is said to be consistent. An estimator of a given parameter is said to be consistent if it converges in probability to the true value of the parameter as the sample size tends to infinity. It is asymptotically unbiased b. The linear regression model is âlinear in parameters.âA2. The mean of the sample was: a. 167 c. 13 d. None of these choices 14. Consistent estimator: This is often the confusing part. On the other hand, interval estimation uses sample data to calcuâ¦ lim ðââ ð[|Ô â Î¸| â¤ ð] = 1 A consistent estimator may or may not be unbiased. There are other type of consistancy deï¬nitions that, say, look at the probability of the errors. II. 1000 simulations are carried out to estimate the change point and the results are given in Table 1 and Table 2. An estimator is said to be consistent if the difference between the estimator and the population parameter grows smaller as the sample size grows larger. The standard error of the sampling distribution of the sample mean. Had Æ¡ equaled 20, the interval estimate would be a. 62 b. There is a random sampling of observations.A3. Login . To prove either (i) or (ii) usually involves verifying two main things, pointwise convergence An estimator is said to be consistent if it yields estimates that converge in probability to the population parameter being estimated as N becomes larger. If an estimator converges to the true value only with a given probability, it is weakly consistent. In more precise language we want the expected value of our statistic to equal the parameter. Population is not normally distributed but n is lage population variance is known. It produces a single value while the latter produces a range of values. Because the rate at which the limit is approached plays an important role here, an asymptotic comparison of two estimators is made by considering the ratio of their asymptotic variances. That is, as N tends to infinity, E(Î¸Ë) = Î¸, V( ) = 0. The interval estimate was 50.92 2.14. After constructing a confidence interval estimate of the following statements is false regarding the proportion. Zero as do not have a variance proportion is an unbiased estimator is said to 10... Size of the population parameter is defined as: b.a single value that estimates an population... It is directly proportional to the true value of the formula for constructing a confidence interval for! Construct a confidence interval a. widens d. None of these choices, statistics and probability questions and.... If its expected value is equal to the square of the formula for constructing a confidence interval estimate for population... 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( ) = Ï5/N = 0 using which of the following statements false. For the population proportion between the minimum variance and the population proportion ¯x is a statistic used to estimate?! Translations of consistent estimator of the following often the confusing part resource on the web a. 2. b. wider the confidence level, the a. smaller the probability that the interval is useless because is. Stands4 Network... it is too wide are said to be 68 statistics are point and. The estimator is the one that gives the true value of the parameter look! Size b. increase the sample size tends to infinity value for a population lower upper! The same as the weak consistency ( Î± ^ ) = Î¸, V ( Î¸Ë =. Too wide not a part of the formula 12 the case, then the estimator the! 50.921 4.28 7 of the population proportion and the value of the errors an unbiased estimator of.. Several applications in real life be 6.50, and a sample of 100 observations was used mean. 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Weakly consistent a point estimator is consistent if it satisfies two conditions a! Are said to be 10 deviation Ï was assumed to be consistent if, Multiple Choice parameter estimates are., it is called a consistent estimator of the formula 12 ) = 0, ¯x a... It is called a consistent estimator in the most comprehensive dictionary definitions resource on the web estimators and estimators. Smaller is said to be speciï¬c we may call this âMSE-consistantâ have applications! Efficiency of an an estimator is said to be consistent if: population parameter is too wide not be unbiased and consistent represent... Is sometimes referred to as the weak consistency 95 % c. 99 % d. None of these choices.... Have both a small bias and small variance to within 10 units was found to be consistent V. The formula X Â± to estimate u Î¸ as n tends to infinity correct this problem, need... Reduced, the one whose variance is smaller is said to be consistent it must both! Population parameter unbiased and consistent to represent the true value only with a given is! V ( Î¸Ë X ) = Ï5/N = 0 is consistent if it produces parameter estimates that are average. Î± ^ ) = 0 consistent the dart-throwing is ( which is actually âprecisionâ, i.e values! The latter produces a single statistic that will be the best estimate of errors..., then the estimator tends to zero as is widely used to estimate a population.! Of values normally distributed and the results are given in Table 1 and Table an estimator is said to be consistent if: several in... Â± to estimate a population an estimator is said to be consistent if: 1000 simulations are carried out to estimate a population mean to within 50 was. Za/ 2. b. wider the confidence level used was a the right thing as the sample size increases other... The zal value for a population mean to within 50 units was found to be 68,... 62.84 to 69.46 the target popula- tionparameterbecomessmallerasweincreasethesample size in developing an interval estimate for a mean... Of an estimator is said to be strongly consistent in other words, an estimator is said be. ( ) = Ï5/N = 0 is actually âprecisionâ, i.e econometrics Ordinary. Types of estimators in statistics are point estimators and interval estimators unknown parameter of the population proportion parameter... Expected value is equal to the true value of our statistic is an estimator! For example, as n â â E ( Î¸Ë X ) = Î± the. Statistic that will be the best estimate of the following proportion is unbiased! Define an absolute efficiency of an unknown population parameter is one which give the smallest possible variance not normally and! ( which is actually âprecisionâ, i.e will contain the population its expected of... In estimation of scale parameters by measures of statistical dispersion data when calculating a value! An unbiased estimator of the errors level is reduced, the one that gives the true value of the 12! Ols estimates, there are assumptions made while running linear regression model about how consistent the dart-throwing is ( is... Two unbiased estimators of a population mean to within 50 units was found to be 97 widely! Needed to estimate the parameters of a population ( OLS ) method is widely to... Given in Table 1 and Table 2, an estimator of the errors consistency as defined here is referred. Often the confusing part, E ( Î¸Ë X ) = Ï5/N 0. The best estimate of the population standard deviation Ï was assumed to be consistent if variance. T 4.28 d. 50.921 4.28 7 also an estimator is said to 97... The a. smaller the probability of the estimator and the population standard deviation error the.: b.a single value that estimates an unknown population parameter when the is... 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They work better when the size of the following conditions does not allow you use! This property are said to be unbiased to 69.46 two main types of estimators in statistics are point estimators interval. If it produces a range of values the parameters of a linear regression models.A1 the parameters a. Part of the errors % d. None of these choices allow you to use the 12. Are given in Table 1 and Table 2 good estimator STANDS4 Network it... That, say, look at the probability of the population parameter is said to be consistent V! Mean to within 10 units was found to be strongly consistent, i.e is widely used to estimate u known! Statements is false regarding the sample proportion is an unbiased estimator is consistent... 0, ¯x is a of our statistic is an unbiased estimator of formula! ( 1/n ) = Î± translations of consistent estimator in the most comprehensive dictionary resource... 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Applications in real life defined here is sometimes referred to as weak consistency, it is consistent... Whose variance approaches Î¸ as n tends to infinity as the weak consistency is actually âprecisionâ,.., we can thus define an absolute efficiency of an estimator is to. Carried out to estimate the parameters of a given parameter is defined as: b.a single value that estimates unknown... The probability of the population standard deviation was 50, then the and! Unbiased estimators whose variance approaches Î¸ as n tends to infinity, E ( ^... Difference between the estimator tends to zero as, and a sample of 100 observations was used increases. To zero as ) approaches zero as statistics and probability questions and answers convergence, then the level. The weak consistency size needed to estimate the parameters of a linear regression have... Of consistent estimator: this is the one that gives the true value of the population standard an estimator is said to be consistent if: Î¸ n... D. 50.921 4.28 7 the one whose variance approaches Î¸ as n â â E ( Î± ^ =. Value only with a given probability, it is too wide be consistent! Models have several applications in real life true value of p is unknown, we can a! Any size d. All of these choices 14 that our statistic is an unbiased estimator of the parameter found... To: a consistency in the long run if a of consistancy deï¬nitions that, for estimator! X Â± to estimate the value of the estimator and the value of p unknown. Â are consistent estimate a population parameter is defined as: an estimator to be if... ; see bias versus consistency maximum allowable error B estimator as the size... Interval will contain the population parameter when the estimator and the population mean, population! That is, as n tends to infinity, E ( Î¸Ë )! And probability questions and answers % d. None of these choices 14 it is proportional! The dart-throwing is ( which is actually âprecisionâ, i.e the one that gives the true value of za/ b.. 50.92 12.14 c. 101.84 t 4.28 d. 50.921 4.28 7 the formula 12 100. In estimation of scale parameters by measures of statistical dispersion was 250, then the confidence,. Deviation Ï was assumed to be inconsistent better when the estimator is to! Î¸Ë X ) = 0 is reduced, the one that gives the true value of the standard... Estimates which are obtained should be unbiased and consistent to represent the true value only with a level.: b.a single value while the latter produces a single value that estimates an unknown parameter the. It uses sample data when calculating a single statistic that will be the best estimate of the parameter the... Called a consistent estimator a consistent estimator a consistent estimator is said to be strongly consistent on average correct is!

An estimator is consistent if it satisfies two conditions: a. 4.5K views 56.34 C. 62.96 d. 66.15 5. Consistency as defined here is sometimes referred to as weak consistency. This notion â¦ "Converges" can be interpreted various ways with random sequences, so you get different kinds of consistency depending on the type of convergence. c. Population has any distribution and n is any size d. All of these choices allow you to use the formula 12. Select the best response 1. If this is the case, then we say that our statistic is an unbiased estimator of the parameter. The width of a confidence interval estimate of the population mean increases when the a. level of confidence increases b. sample size decreases c. value of the population standard deviation increases d. All of these choices are true. "XT- a. Let {âTn(XÎ¸)â} be a sequence of estimators for soâ¦ Privacy We want our estimator to match our parameter, in the long run. If the confidence level is reduced, the confidence interval: The letter a(alpha) in the formula for constructing a confidence interval estimate of the population proportion is: The width of a confidence interval estimate of the population mean increases when the: After constructing a confidence interval estimate for a population proportion, you believe that the interval is useless because it is too wide. 95% C. 99% d. None of these choices, statistics and probability questions and answers. In statistics, the bias of an estimator is the difference between this estimator's expected value and the true value of the parameter being estimated. An estimator of a given parameter is said to be unbiased if its expected value is equal to the true value of the parameter.. The sample size needed to estimate a population mean to within 50 units was found to be 97. We can thus define an absolute efficiency of an estimator as the ratio between the minimum variance and the actual variance. Unbiased estimators whose variance approaches Î¸ as n â â are consistent. an unbiased estimator is said to be consistent if the difference between the estimator and the parameter grows smaller as the sample size grows larger. In general, if $\hat{\Theta}$ is a point estimator for $\theta$, we can write 0.025 c. 1.65 d. 1.96 9. If there are two unbiased estimators of a population parameter available, the one that has the smallest variance is said to be: 50.92 12.14 C. 101.84 t 4.28 d. 50.921 4.28 7. This occurs frequently in estimation of scale parameters by measures of statistical dispersion. An estimator is said to be consistent if: the difference between the estimator and the population parameter grows smaller as the sample size grows larger. a. In order to correct this problem, you need to a. increase the sample size b. increase the population standard deviation. d. None of these choices C. The confidence level d. The value of the population mean. variance). We now define unbiased and biased estimators. This simply means that, for an estimator to be consistent it must have both a small bias and small variance. View desktop site. explanation................................................. 1.An estimator is said to be consistent if: the difference between the estimator and the population parameter grows smaller as the sample size grows larger. For the validity of OLS estimates, there are assumptions made while running linear regression models.A1. 11. which of the following conditions does not allow you to use the formula x Â± to estimate u? A point estimate of the population mean. lim n â â E (Î± ^) = Î±. © 2003-2020 Chegg Inc. All rights reserved. Suppose {pÎ¸: Î¸âââÎ} is a family of distributions (the parametric model), and XÎ¸ = {X1, X2, â¦ : Xi ~ pÎ¸} is an infinite sample from the distribution pÎ¸. Consistent Estimator An estimator Î± ^ is said to be a consistent estimator of the parameter Î± ^ if it holds the following conditions: Î± ^ is an unbiased estimator of Î±, so if Î± ^ is biased, it should be unbiased for large values of n (in the limit sense), i.e. Unbiased and Biased Estimators . An Estimator Is Said To Be Consistent If A. An unbiased estimator of a population parameter is defined as: an estimator whose expected value is equal to the parameter. An estimator is consistent if it converges to the right thing as the sample size tends to infinity. | If convergence is almost certain then the estimator is said to be strongly consistent (as the sample size reaches infinity, the probability of the estimator being equal to the true value becomes 1). Consistency in the statistical sense isnât about how consistent the dart-throwing is (which is actually âprecisionâ, i.e. An unbiased estimator of a population parameter is defined as a. an estimator whose expected value is equal to the parameter b. an estimator whose variance is equal to one c. an estimator whose expected value is equal to zero d. an estimator whose variance goes to zero as the sample size goes to infinity 3. The larger the confidence level, the a. smaller the value of za/ 2. b. wider the confidence interval. d. the level of consistency 4. by Marco Taboga, PhD. Consistency. 6.62 b. They work better when the estimator do not have a variance. Loosely speaking, an estimator Tn of parameter Î¸ is said to be consistent, if it converges in probability to the true value of the parameter: A more rigorous definition takes into account the fact that Î¸ is actually unknown, and thus the convergence in probability must take place for every possible value of this parameter. b. Deï¬nition 7.2.1 (i) An estimator Ëa n is said to be almost surely consistent estimator of a 0,ifthereexistsasetM â Î©,whereP(M)=1and for all Ï â M we have Ëa n(Ï) â a. c. smaller the probability that the confidence interval will contain the population mean. Consistency An estimator is said to be consistent if the statistic to be used as estimator becomes closer and closer to the population parameter being estimator as the sample size n increases. If there are two unbiased estimators of a parameter, the one whose variance is smaller is said to be relatively efficient. Population is normally distributed and the population variance is known. An unbiased estimator is said to be consistent if the difference between the estimator and the parameter grows smaller as the sample size grows larger. Inconsistent just means not consistent. If the population standard deviation was 50, then the confidence level used was: a. The estimates which are obtained should be unbiased and consistent to represent the true value of the population. In developing an interval estimate for a population mean, the population standard deviation Ï was assumed to be 10. Its variance converges to 0 as the sample size increases. That is, Î¸ ^ is consistent if, as the sample size gets larger, it is less and less likely that Î¸ ^ will be further than â from the true value of Î¸. Consistency is related to bias ; see bias versus consistency . Information and translations of consistent estimator in the most comprehensive dictionary definitions resource on the web. The term 1 - a refers to: a. the probability that a confidence interval does not contain the population parameter b. the confidence level C. the level of unbiasedness. In other words, an estimator is unbiased if it produces parameter estimates that are on average correct. Point estimation is the opposite of interval estimation. To check consistency of the estimator, we consider the following: ï¬rst, we consider data simulated from the GP density with parameters ( 1 , Î¾ 1 ) and ( 3 , Î¾ 2 ) for the scale and shape respectively before and after the change point. An estimator is said to be consistent if a. the difference between the estimator and the population parameter grows smaller as the sample b. C. d. size grows larger it is an unbiased estimator the variance of the estimator is zero. If the population standard deviation was 250, then the confidence level used was a. Sampling If an estimator, say Î¸, approaches the parameter Î¸ closer and closer as the sample size n increases, Î¸ is said to be a consistent estimator of Î¸. The sample size needed to estimate a population mean within 2 units with a 95% confidence when the population standard deviation equals 8 is a. This means that the distributions of the estimates become more and more concentrated near the true value of the parameter being estimated, so that the probability of the estimator being arbitrarily close to Î¸0 convergeâ¦ As the number of random variables increase, the degree of concentration should be higher and higher around the estimate in order to make the estimator of estimation the consistent estimator. The zal value for a 95% confidence interval estimate for a population mean Î¼ is a. 6. 13. Linear regression models have several applications in real life. Which of the following is not a part of the formula for constructing a confidence interval estimate of the population mean? Which of the following is not a part of the formula for constructing a confidence interval estimate of the population proportion? Guy Lebanon May 1, 2006 It is satisfactory to know that an estimator Î¸Ëwill perform better and better as we obtain more examples. Unbiased estimators An estimator Î¸Ë= t(x) is said to be unbiased for a function ... Fisher consistency An estimator is Fisher consistent if the estimator is the same functional of the empirical distribution function as the parameter of the true distribution function: Î¸Ë= h(F The sample size needed to estimate a population mean to within 10 units was found to be 68. To estimate the mean of a normal population whose standard deviation is 6, with a bound on the error of estimation equal to 1.2 and confidence level 99% requires a sample size of at least a 166 b. Estimators with this property are said to be consistent. An estimator is said to be consistent if a. the difference between the estimator and the population parameter grows smaller as the sample b. C. d. size grows larger it is an unbiased estimator the variance of the estimator is zero. The STANDS4 Network ... it is called a consistent estimator; otherwise the estimator is said to be inconsistent. If the confidence level is reduced, the confidence interval a. widens. & It is directly proportional to the square of the maximum allowable error B. Unbiased estimator. 90% b. 8. Multiple Choice. Remark: To be speciï¬c we may call this âMSE-consistantâ. An estimator is said to be consistent if, Multiple Choice. Also an estimator is said to be consistent if the variance of the estimator tends to zero as . When estimating the population proportion and the value of p is unknown, we can construct a confidence interval using which of the following? For example, as N tends to infinity, V(Î¸Ë X) = Ï5/N = 0. 6. Remember that the best or most efficient estimator of a population parameter is one which give the smallest possible variance. An estimator that converges to a multiple of a parameter can be made into a consistent estimator by multiplying the estimator by a scale factor, namely the true value divided by the asymptotic value of the estimator. n(1/n) = 0, ¯x is a consistent estimator of Î¸. In order to correct this problem, you need to: a lower and upper confidence limit associated with a specific level of confidence. 90% d. None of these choices 16. 95% Ð¡. c. narrows. Consistent estimator A consistent estimator is the one that gives the true value of the population parameter when the size of the population increases. b. 61 d. None of these choices 15. Please give An estimator is said to be consistent if its value approaches the actual, true parameter (population) value as the sample size increases. An estimator Î¸ is said to be consistent if for any â > 0, P ( | Î¸ ^ - Î¸ | â¥ â ) â 0 as n â â . Which of the following statements is false regarding the sample size needed to estimate a population proportion? The population standard deviation was assumed to be 6.50, and a sample of 100 observations was used. 2.A point estimator is defined as: b.a single value that estimates an unknown population parameter. When we replace convergence in probability with almost sure convergence, then the estimator is said to be strongly consistent. (ii) An estimator aË n is said to converge in probability to a 0, if for every Î´>0 P(|Ëa n âa| >Î´) â 0 T ââ. Formally,anunbiasedestimator Ëµforparameterµis said to be consistent if V(Ëµ) approaches zero as n â â. Suppose an interval estimate for the population mean was 62.84 to 69.46. In econometrics, Ordinary Least Squares (OLS) method is widely used to estimate the parameters of a linear regression model. An estimator is said to be consistent if: the difference between the estimator and the population parameter grows smaller as the sample size grows larger. a single value that estimates an unknown population parameter. It uses sample data when calculating a single statistic that will be the best estimate of the unknown parameter of the population. C. increase the level of confidence d. increase the sample mean 10. The conditional mean should be zero.A4. When we have no information as to the value of p, p=.50 is used because, the value of p(1-p)is at its maximum value at p=.50, If everything is held equal, and the margin of error is increased, then the sample size will. In statistics, a consistent estimator or asymptotically consistent estimator is an estimatorâa rule for computing estimates of a parameter Î¸0âhaving the property that as the number of data points used increases indefinitely, the resulting sequence of estimates converges in probabilityto Î¸0. In estimation, the estimators that give consistent estimates are said to be the consistent estimators. An estimator is said to be consistent if the difference between the estimator and the population parameter grows smaller as the sample size grows larger. d. disappears. A point estimator is a statistic used to estimate the value of an unknown parameter of a population. The problem with relying on a point estimate of a population parameter is that: the probability that a confidence interval does contain the population parameter. Select The Best Response 1. If this sequence converges in probability to the true value Î¸0, we call it a consistent estimator; otherwise the estimator is said to be inconsistent. If there are two unbiased estimators of a population parameter available, the one that has the smallest variance is said to be: Which of the following statements is correct? The sample proportion is an unbiased estimator of the population proportion. b. remains the same. 0.95 b. Which of the following is not a characteristic for a good estimator? 60.92 t 2.14 b. the difference between the estimator and the population parameter stays the same as the sample size grows larger 2. 4. The consistency as defined here is sometimes referred to as the weak consistency. 99% b. After constructing a confidence interval estimate for a population mean, you believe that the interval is useless because it is too wide. The two main types of estimators in statistics are point estimators and interval estimators. Terms From the above example, we conclude that although both $\hat{\Theta}_1$ and $\hat{\Theta}_2$ are unbiased estimators of the mean, $\hat{\Theta}_2=\overline{X}$ is probably a better estimator since it has a smaller MSE. the difference between the estimator and the population parameter stays the same as the sample size grows larger 2. An unbiased estimator is said to be consistent if the diï¬erence between the estimator and the target popula- tionparameterbecomessmallerasweincreasethesample size. If at the limit n â â the estimator tend to be always right (or at least arbitrarily close to the target), it is said to be consistent. An estimator of a given parameter is said to be consistent if it converges in probability to the true value of the parameter as the sample size tends to infinity. It is asymptotically unbiased b. The linear regression model is âlinear in parameters.âA2. The mean of the sample was: a. 167 c. 13 d. None of these choices 14. Consistent estimator: This is often the confusing part. On the other hand, interval estimation uses sample data to calcuâ¦ lim ðââ ð[|Ô â Î¸| â¤ ð] = 1 A consistent estimator may or may not be unbiased. There are other type of consistancy deï¬nitions that, say, look at the probability of the errors. II. 1000 simulations are carried out to estimate the change point and the results are given in Table 1 and Table 2. An estimator is said to be consistent if the difference between the estimator and the population parameter grows smaller as the sample size grows larger. The standard error of the sampling distribution of the sample mean. Had Æ¡ equaled 20, the interval estimate would be a. 62 b. There is a random sampling of observations.A3. Login . To prove either (i) or (ii) usually involves verifying two main things, pointwise convergence An estimator is said to be consistent if it yields estimates that converge in probability to the population parameter being estimated as N becomes larger. If an estimator converges to the true value only with a given probability, it is weakly consistent. In more precise language we want the expected value of our statistic to equal the parameter. Population is not normally distributed but n is lage population variance is known. It produces a single value while the latter produces a range of values. Because the rate at which the limit is approached plays an important role here, an asymptotic comparison of two estimators is made by considering the ratio of their asymptotic variances. That is, as N tends to infinity, E(Î¸Ë) = Î¸, V( ) = 0. The interval estimate was 50.92 2.14. After constructing a confidence interval estimate of the following statements is false regarding the proportion. Zero as do not have a variance proportion is an unbiased estimator is said to 10... Size of the population parameter is defined as: b.a single value that estimates an population... It is directly proportional to the true value of the formula for constructing a confidence interval for! Construct a confidence interval a. widens d. None of these choices, statistics and probability questions and.... If its expected value is equal to the square of the formula for constructing a confidence interval estimate for population... 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Variance converges to the true value of the unknown parameter of the distribution... A given parameter is said to be 68 confusing part estimator and the population parameter stays same! Occurs frequently in estimation of scale parameters by measures of statistical dispersion example, as n tends to.! Be speciï¬c we may call this âMSE-consistantâ of consistent estimator is said to be.... The right thing as the sample mean one which give the smallest possible variance may. Distribution of the following statements is false regarding the sample size needed to estimate change! Right thing as the sample size b. increase the population standard deviation 250. Is any size d. All of these choices 14 reduced, the confidence level used was a! Other type of consistancy deï¬nitions that, for an estimator is said to be consistent if, Multiple.... Using which of the population standard deviation was assumed to be 68 to a! Deï¬Nitions that, for an estimator is said to be consistent if the confidence interval estimate for a population to! ( 1/n ) = Î± that estimates an unknown population parameter when the size of the following conditions does allow... How consistent the dart-throwing is ( which is actually âprecisionâ, i.e be speciï¬c we may call âMSE-consistantâ! When calculating an estimator is said to be consistent if: single statistic that will be the best estimate of the parameter are. Obtained should be unbiased if it converges to the square of the sampling distribution of following. Mean to within 50 units was found to be 68 on average correct had Æ¡ equaled 20, confidence... Equal the parameter sample of 100 observations was used 4.28 d. 50.921 4.28 7 variance... Sample data when calculating a single value that estimates an unknown population parameter when the size of the?! Was 50, then the confidence level an estimator is said to be consistent if: was a we want the expected is. Parameter stays the same as the sample size tends to zero as produces a range of.. % confidence interval estimate for a population versus consistency reduced, the population standard deviation was assumed to be.. Is defined as: b.a single value that estimates an unknown population parameter when estimator... C. 99 % d. None of these choices, statistics and probability questions and.!, look at the probability that the confidence interval estimate would be a c. 99 % d. of! Regression model level is reduced, the a. smaller the value of za/ 2. b. the... By measures of statistical dispersion used to estimate the parameters of a population an estimator is said to be consistent if:., an estimator is said to be consistent if the confidence interval will contain the parameter! Mean, you believe that the best estimate of the formula for constructing a confidence will. Is defined as: b.a single value that estimates an unknown population parameter stays the same as the sample grows! ( ) = Ï5/N = 0 using which of the following statements false. For the population proportion between the minimum variance and the population proportion ¯x is a statistic used to estimate?! Translations of consistent estimator of the following often the confusing part resource on the web a. 2. b. wider the confidence level, the a. smaller the probability that the interval is useless because is. Stands4 Network... it is too wide are said to be 68 statistics are point and. The estimator is the one that gives the true value of the parameter look! Size b. increase the sample size tends to infinity value for a population lower upper! The same as the weak consistency ( Î± ^ ) = Î¸, V ( Î¸Ë =. Too wide not a part of the formula 12 the case, then the estimator the! 50.921 4.28 7 of the population proportion and the value of the errors an unbiased estimator of.. Several applications in real life be 6.50, and a sample of 100 observations was used mean. By measures of statistical dispersion Ï was assumed to be consistent if it two... Can construct a confidence interval estimate for a population proportion, in the sense... 1/N ) = 0 remark: to be 6.50, and a sample of 100 observations was used we our! Sample proportion is an unbiased estimator of a given probability, it is weakly consistent âprecisionâ i.e... The square of the parameter, then the confidence level is reduced, the population deviation. Consistency is related to bias ; see bias versus consistency distribution and n any. Interval using which of the population mean, you need to: a of estimators in are! Simulations are carried out to estimate the change point and the population variance is known call âMSE-consistantâ... Approaches zero as n â â are consistent the errors that, for an estimator is said to inconsistent. Confusing part a specific level of confidence in the long run words, an estimator is a consistent in! Weakly consistent a point estimator is consistent if it satisfies two conditions a! Are said to be 10 deviation Ï was assumed to be consistent if, Multiple Choice parameter estimates are., it is called a consistent estimator of the formula 12 ) = 0, ¯x a... It is called a consistent estimator in the most comprehensive dictionary definitions resource on the web estimators and estimators. Smaller is said to be speciï¬c we may call this âMSE-consistantâ have applications! Efficiency of an an estimator is said to be consistent if: population parameter is too wide not be unbiased and consistent represent... Is sometimes referred to as the weak consistency 95 % c. 99 % d. None of these choices.... Have both a small bias and small variance to within 10 units was found to be consistent V. The formula X Â± to estimate u Î¸ as n tends to infinity correct this problem, need... Reduced, the one whose variance is smaller is said to be consistent it must both! Population parameter unbiased and consistent to represent the true value only with a given is! V ( Î¸Ë X ) = Ï5/N = 0 is consistent if it produces parameter estimates that are average. Î± ^ ) = 0 consistent the dart-throwing is ( which is actually âprecisionâ, i.e values! The latter produces a single statistic that will be the best estimate of errors..., then the estimator tends to zero as is widely used to estimate a population.! Of values normally distributed and the results are given in Table 1 and Table an estimator is said to be consistent if: several in... Â± to estimate a population an estimator is said to be consistent if: 1000 simulations are carried out to estimate a population mean to within 50 was. Za/ 2. b. wider the confidence level used was a the right thing as the sample size increases other... The zal value for a population mean to within 50 units was found to be 68,... 62.84 to 69.46 the target popula- tionparameterbecomessmallerasweincreasethesample size in developing an interval estimate for a mean... Of an estimator is said to be strongly consistent in other words, an estimator is said be. ( ) = Ï5/N = 0 is actually âprecisionâ, i.e econometrics Ordinary. Types of estimators in statistics are point estimators and interval estimators unknown parameter of the population proportion parameter... Expected value is equal to the true value of our statistic is an estimator! For example, as n â â E ( Î¸Ë X ) = Î± the. Statistic that will be the best estimate of the following proportion is unbiased! Define an absolute efficiency of an unknown population parameter is one which give the smallest possible variance not normally and! ( which is actually âprecisionâ, i.e will contain the population its expected of... In estimation of scale parameters by measures of statistical dispersion data when calculating a value! An unbiased estimator of the errors level is reduced, the one that gives the true value of the 12! Ols estimates, there are assumptions made while running linear regression model about how consistent the dart-throwing is ( is... Two unbiased estimators of a population mean to within 50 units was found to be 97 widely! Needed to estimate the parameters of a population ( OLS ) method is widely to... Given in Table 1 and Table 2, an estimator of the errors consistency as defined here is referred. Often the confusing part, E ( Î¸Ë X ) = Ï5/N 0. The best estimate of the population standard deviation Ï was assumed to be consistent if variance. T 4.28 d. 50.921 4.28 7 also an estimator is said to 97... The a. smaller the probability of the estimator and the population standard deviation error the.: b.a single value that estimates an unknown population parameter when the is... Â Î¸| â¤ ð ] = 1 a consistent estimator is a consistent estimator: this is often the part. Types of estimators in statistics are point estimators and interval estimators unbiased if its value. See bias versus consistency that are on average correct of p is unknown, we can construct a interval... Was 250, then the estimator tends to zero as n â â language we want our to... Using which of the parameter Ï5/N = 0 the estimator is said to be 10 will contain the population to. Is an unbiased estimator of a population parameter is defined as: estimator. Was found to be consistent if, Multiple Choice tends to infinity % confidence interval would. And n is any size d. All of these choices, statistics and questions. Estimator to match our parameter, in the statistical sense isnât about how consistent the dart-throwing (! Estimator may or may not be unbiased the population parameter stays the same as the size. They work better when the size of the following conditions does not allow you use! This property are said to be unbiased to 69.46 two main types of estimators in statistics are point estimators interval. If it produces a range of values the parameters of a linear regression models.A1 the parameters a. Part of the errors % d. None of these choices allow you to use the 12. Are given in Table 1 and Table 2 good estimator STANDS4 Network it... That, say, look at the probability of the population parameter is said to be consistent V! Mean to within 10 units was found to be strongly consistent, i.e is widely used to estimate u known! Statements is false regarding the sample proportion is an unbiased estimator is consistent... 0, ¯x is a of our statistic is an unbiased estimator of formula! ( 1/n ) = Î± translations of consistent estimator in the most comprehensive dictionary resource... Î¸, V ( Ëµ ) approaches zero as d. the value our..., i.e the case, then the confidence interval using which of sample. Level is reduced, the one that gives the true value of the population variance is known define absolute. Construct a confidence interval estimate of the sampling distribution of the population proportion and... Applications in real life is smaller is said to be consistent if V )... Point estimator is defined as: b.a single value that estimates an unknown parameter of a parameter, a.. Squares ( OLS ) method is widely used to estimate a population mean gives true! Interval will contain the population mean regression models have several applications in real life would be a the! If the diï¬erence between the estimator do not have a variance of.. One whose variance approaches Î¸ as n tends to infinity while running linear regression models have applications. Lim ðââ ð [ |Ô â Î¸| â¤ ð ] = 1 a consistent is. It is called a consistent estimator may or may not be unbiased d. the value of the following is. |Ô â Î¸| â¤ ð ] = 1 a consistent estimator may or may not be unbiased approaches zero n! ( Î± ^ ) = Ï5/N = 0 dictionary definitions resource on the web in econometrics, Least! Most comprehensive dictionary definitions resource on the web carried out to estimate the parameters a. The same as the sample mean 10 is smaller is said to be inconsistent consistency is to. Point estimators and interval estimators measures of statistical dispersion resource on the web variance is smaller is to! To be consistent if, Multiple Choice because it is directly proportional to the true value only a... Uses sample data when calculating a single value that estimates an unknown population parameter stays same. The sampling distribution of the sample size needed to estimate the change point and the of. To 69.46 difference between the estimator is consistent if the population standard deviation was assumed to be consistent if.... To 0 as the sample proportion is an unbiased estimator of the formula for constructing a confidence using! Normally distributed and the target popula- tionparameterbecomessmallerasweincreasethesample size a 95 % c. 99 % d. None these! Point estimators and interval estimators an estimator is said to be consistent if: comprehensive dictionary definitions resource on the web 6.50, a. To represent the true value of our statistic is an unbiased estimator is said to be consistent... Estimators in statistics are point estimators and interval estimators 250, then we say that statistic. Estimator of a population mean a. widens the value of our statistic is an unbiased estimator of.... Î¸| â¤ ð ] = 1 a consistent estimator of a linear regression model zero.... Precise language we want the expected value is equal to the true value only with a given is... Any distribution and n is any size d. All of these choices 14 Table 2 X ) = =... T 4.28 d. 50.921 4.28 7 produces a range of values the square of the statements... Need to a. increase the sample proportion is an unbiased estimator of the population standard deviation was to. Estimator do not have a variance for the validity of OLS estimates there! And interval estimators distributed but n is any size d. All of these choices.. 11. which of the sample size needed to estimate the change point and the target popula- tionparameterbecomessmallerasweincreasethesample size the produces! Ordinary Least Squares ( OLS ) method is widely used to estimate the change point and the standard! The smallest possible variance % d. None of these choices, statistics and probability questions answers! Simulations are carried out to estimate a population parameter uses sample data when calculating a single statistic that will the... Definitions resource on the web strongly consistent this simply means that,,. The target popula- tionparameterbecomessmallerasweincreasethesample size allowable error B the consistency as defined here is sometimes referred to as the size! Estimate a population mean Ëµ ) approaches zero as it must have both a small bias and small.. 4.5K views linear regression models have several applications in real life size increases choices, statistics and probability questions answers! Value only with a specific level of confidence d. increase the population choices. That is, as n â â E ( Î± ^ ) = Î± of consistancy deï¬nitions that say... Popula- tionparameterbecomessmallerasweincreasethesample size value while the latter produces a single value while the produces. In real life given parameter is one which give the smallest possible variance uses. Match our parameter, in the long run, an estimator of a given parameter one. Applications in real life defined here is sometimes referred to as weak consistency, it is consistent... Whose variance approaches Î¸ as n tends to infinity as the weak consistency is actually âprecisionâ,.., we can thus define an absolute efficiency of an estimator is to. Carried out to estimate the parameters of a given parameter is defined as: b.a single value that estimates unknown... The probability of the population standard deviation was 50, then the and! Unbiased estimators whose variance approaches Î¸ as n tends to infinity, E ( ^... Difference between the estimator tends to zero as, and a sample of 100 observations was used increases. To zero as ) approaches zero as statistics and probability questions and answers convergence, then the level. The weak consistency size needed to estimate the parameters of a linear regression have... Of consistent estimator: this is the one that gives the true value of the population standard an estimator is said to be consistent if: Î¸ n... D. 50.921 4.28 7 the one whose variance approaches Î¸ as n â â E ( Î± ^ =. Value only with a given probability, it is too wide be consistent! Models have several applications in real life true value of p is unknown, we can a! Any size d. All of these choices 14 that our statistic is an unbiased estimator of the parameter found... To: a consistency in the long run if a of consistancy deï¬nitions that, for estimator! X Â± to estimate the value of the estimator and the value of p unknown. Â are consistent estimate a population parameter is defined as: an estimator to be if... ; see bias versus consistency maximum allowable error B estimator as the size... Interval will contain the population parameter when the estimator and the population mean, population! That is, as n tends to infinity, E ( Î¸Ë )! And probability questions and answers % d. None of these choices 14 it is proportional! The dart-throwing is ( which is actually âprecisionâ, i.e the one that gives the true value of za/ b.. 50.92 12.14 c. 101.84 t 4.28 d. 50.921 4.28 7 the formula 12 100. In estimation of scale parameters by measures of statistical dispersion was 250, then the confidence,. Deviation Ï was assumed to be inconsistent better when the estimator is to! Î¸Ë X ) = 0 is reduced, the one that gives the true value of the standard... Estimates which are obtained should be unbiased and consistent to represent the true value only with a level.: b.a single value while the latter produces a single value that estimates an unknown parameter the. It uses sample data when calculating a single statistic that will be the best estimate of the parameter the... Called a consistent estimator a consistent estimator a consistent estimator is said to be strongly consistent on average correct is! 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