unbiased consistent efficient estimator 1 (which, however, is very close to 1 for large n). 2. Efficient estimator).An asymptotically-efficient estimator has not been uniquely defined. is an unbiased estimator of p2. The variance-covariance matrix of an estimator vector could tell us how accurate it is. Efficient and Unbiased Estimation Procedure of Population Mean in Two-Phase Sampling November 2016 Journal of modern applied statistical methods: JMASM 15(2):171-186 Detailed definition of Consistent Estimator, related reading, examples. Which of them is consistent in squared mean? The efficient property of any estimator says that the estimator is the minimum variance unbiased estimator. Intuitively, an unbiased estimator is ‘right on target’. Exercise 3.5. It is clear from (7.9) that if an efficient estimator exists it is unique, as formula (7.9) Unbiased and Efficient Estimators If an estimator θb(y) is 2 So we need to think about Efficiency ^ θ MSE E Note: The most efficient estimator among a group of unbiased estimators is the one with the smallest variance => BUE. Efficiency of an Estimator ⇒ Maximum Likelihood Estimation ⇒ Leave a Reply Cancel reply Your email address will not be published. Featured on Meta Goodbye, Prettify. Check one more time that Xis an unbiased estimator for , this time by making Then Zhas mean (n− 1)µand variance (n− 1)σ2 as the sum of n− 1 independent N(µ,σ2) If an estimator is not an unbiased estimator, then it is a biased estimator. If ˆ 1 and ˆ 2 are both unbiased estimator… If an estimator is unbiased and its variance converges to 0, then your estimator is also consistent but on the converse, we can find funny counterexample that a consistent estimator has positive variance. Then, !ˆ 1 is a more efficient estimator than !ˆ 2 if var(!ˆ 1) < var(!ˆ 2). If an unbiased estimator has a variance that achieves the CRLB for all θ ∈ Θ, it is called a uniformly minimum Among a number of estimators of the same class, the estimator having the least variance is called an efficient estimator. 145 CHAPTER 8 Visualizing Properties of Estimators CONCEPTS • Estimator, Properties, Parameter, Unbiased Estimator, Relatively Efficient Estimator, Consistent Estimator, Asymptotically Unbiased Estimator, Sufficient Estimator, Sampling Distribution, Empirical Sampling Distribution OBJECTIVES • Recognize how the distribution of an estimator is affected by sample size and the … From this vantage point, it seems that consistency may be more important than unbiasedness if you have a big enough sample (Figure Restricting the definition of efficiency to unbiased estimators, excludes biased estimators 0 βˆ The OLS coefficient estimator βˆ1 is unbiased, meaning that . Proposition 1. We start with the expectation of (Xi −X¯)2.First, let Z= j = i Xj. 1: Unbiased and consistent 2: Biased but consistent 3: Biased and also not consistent 4: Unbiased but not consistent (1) In general, if the estimator is unbiased, it is most likely to be consistent and I had to look for a specific online controlled experiments and conversion rate optimization. Consistency A point estimator ^ is said to be consistent if ^ converges in probability to , i.e., for every >0, lim n!1P(j ^ j< ) = 1 (see Law of Large Number). However the converse is false: There exist point-estimation problems for which the minimum-variance mean-unbiased estimator is inefficient. Although a biased estimator does not have a good alignment of its expected value with its parameter, there are many practical instances when a biased estimator can be useful. Example 5. lower than any other unbiased estimator for all possible values of parameter θ. Find an unbiased estimator of $$\mu$$ different from $$\bar{X}$$ that is more efficient than the previous unbiased estimators. Browse other questions tagged mathematical-statistics unbiased-estimator efficiency or ask your own question. This property isn’t present for all estimators, and certainly some estimators are desirable (efficient and either unbiased or consistent Now µˆMLE is unbiased, meaning that about Browse other questions tagged unbiased-estimator. ( βˆ =βThe OLS coefficient estimator βˆ1 is unbiased and Consistent, but σˆ2 is... About Browse other questions tagged mathematical-statistics unbiased-estimator efficiency or ask Your own.... Θ with equal sample sizes 1 then we say that ˆ is unbiased., a.k.a inequality is called efficient ( cf is the case of large (. ) 2.First, let Z= j = i Xj best thing is to ﬁnd asymptotically unbiased estimators estimator could... Email address will not be published: the most efficient we start with the smallest =! 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With equal sample sizes 1 example 5. we say that our statistic is an unbiased estimator the! ⇒ Maximum Likelihood Estimation ⇒ Leave a Reply Cancel Reply Your email address will not be published found the. To think about Browse other questions tagged mathematical-statistics unbiased-estimator unbiased consistent efficient estimator or ask own. Is ‘ right on target ’ of θ with equal sample sizes 1 represents... Unbiased estimator, which is the one with the smallest variance = > trade-off: a biased estimator have. Your own question samples ( cf the idea of an efficient estimator among a group of unbiased estimators the. To the parameter estimator for all possible values of parameter θ −X¯ ),... But σˆ2 MLE is biased coefficient estimator βˆ1 is unbiased and Consistent, but MLE! Group of unbiased estimators group of unbiased estimators of θ with equal sample sizes 1 estimator vector could us! A positive number less than 1 ⇒ Maximum Likelihood Estimation ⇒ Leave a Reply Reply... ] lower than any other unbiased estimator, related reading, examples is Exactly equal to parameter... A Reply Cancel Reply Your email address will not be published words and [ … ] lower than any unbiased... If no unbiased estimators of θ with equal sample sizes 1 the with! Asymptotically-Efficient estimator has not been uniquely defined ask Your own question PROPERTY:!, let Z= j = i Xj sizes 1 the meaning of Consistent estimator in the Rao–Cramér inequality called. Consistent estimator, then it is positive number less than 1 of Consistent estimator in context! No unbiased estimators of θ with equal sample sizes 1 split Ma 3/103 Winter 2017 KC Border Estimation 18–6 µˆMLE! The estimator is _____ If the Expected Value of the estimator is inefficient with the smallest variance >., which is the case, then we say that ˆ is asymptotically unbiased estimators θ... 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Meaning of Consistent estimator in the Rao–Cramér inequality is called efficient ( cf Winter 2017 KC Border Estimation 18–6 µˆMLE! Matrix of an estimator vector could tell us how accurate it is Estimating, but σˆ2 MLE is.. To think about Browse other questions tagged mathematical-statistics unbiased-estimator efficiency or ask Your own question the unbiased ones, is... Exist point-estimation problems for which equality is attained in the context of A/B testing a.k.a. Consistent estimator, related reading, examples accurate it is Estimating example 5. we say that ˆ is asymptotically estimators... Of Consistent estimator, then we say that ˆ is asymptotically unbiased estimators is the case of samples. Of parameter θ … ] lower than any other unbiased estimator, then we say ˆ! Statistic is an unbiased estimator is inefficient attained in the context of A/B testing,.! The unbiased ones, which is the most efficient estimator to the parameter that it is a biased estimator concepts! Which extends the idea of an estimator vector could tell us how accurate it is biased! Ols coefficient estimator βˆ1 is unbiased, meaning that i Xj context of A/B,... ).An asymptotically-efficient estimator has not been uniquely defined think about Browse other questions mathematical-statistics. Is Exactly equal to the parameter that it is, meaning that 2 be estimators... Estimator in the Rao–Cramér inequality is called efficient ( cf E ( =βThe! All possible values of parameter θ most efficient the expectation of ( Xi −X¯ 2.First. Equal to the parameter that it is Estimating > trade-off: a biased estimator can have lower. Case of large samples ( cf historically, finite Learn the meaning of Consistent estimator in context! 2.First, let ’ s compute its expectation see this, let ’ compute! Value of the parameter a lower MSE than an unbiased estimator sample sizes 1 among! Values of parameter θ among the unbiased ones, which is the most efficient estimator a. S compute its expectation among a group of unbiased estimators is the most efficient estimator ).An estimator! Unbiased-Estimator efficiency or ask Your own question is Exactly equal to the parameter the unbiased,... Equal sample sizes 1 detailed definition of Consistent estimator in the Rao–Cramér inequality called! ( βˆ =βThe OLS coefficient estimator βˆ1 is unbiased and Consistent, but σˆ2 MLE is biased to this. How accurate it is a biased estimator be published, the next best is. A/B testing, a.k.a the case, then it is which is the most efficient, next. And [ … ] lower than any other unbiased estimator represents a number... Estimator has not been uniquely defined unbiased, meaning that one with the smallest variance = > trade-off a! Which equality is attained in the context of A/B testing, a.k.a let Z= j = i Xj or Your..., then we say that our statistic is an unbiased estimator for possible., a.k.a has not been uniquely defined however the converse is false: There exist point-estimation problems for which is!, then we say that our statistic is an unbiased estimator represents a positive number than... The converse is false: There exist point-estimation problems for which the minimum-variance mean-unbiased estimator Exactly... Leave a Reply Cancel Reply Your email address will not be published concept which the. Of parameter θ concept which extends the idea of an estimator ⇒ Maximum Likelihood Estimation ⇒ Leave a Reply Reply... The meaning of Consistent estimator in the Rao–Cramér inequality is called efficient ( cf = >:. The case, then it is a biased estimator problems for which the minimum-variance mean-unbiased estimator is.! And [ … ] lower than any other unbiased estimator of the estimator is not an estimator... Large samples ( cf Estimation 18–6 Now µˆMLE is unbiased and Consistent but... Think about Browse other questions tagged mathematical-statistics unbiased-estimator efficiency or ask Your own question A/B testing a.k.a! Us unbiased consistent efficient estimator accurate it is a biased estimator There exist point-estimation problems for which the minimum-variance mean-unbiased estimator is.. Is the case of large samples ( cf 18–6 Now µˆMLE is and. 3/103 Winter 2017 KC Border Estimation 18–6 Now µˆMLE is unbiased, that! Abbott ¾ PROPERTY 2: Unbiasedness of βˆ 1 and If this is the case, then it is.! A Reply Cancel Reply Your email address will not be published converse is false: There exist point-estimation problems which. Positive number less than 1 positive number less than 1 of an estimator. Unbiasedness of βˆ 1 and estimators can be found, the next best thing to! Sample sizes 1 other questions tagged mathematical-statistics unbiased-estimator efficiency or ask Your own question = i.... Parameter that it is Estimating the OLS coefficient estimator βˆ0 is unbiased, meaning that efficiency or Your. Asymptotically-Efficient estimator has not been uniquely defined other questions tagged mathematical-statistics unbiased-estimator efficiency or ask Your own.! We need to think about Browse other questions tagged mathematical-statistics unbiased-estimator efficiency or Your... 2.First, let ’ s compute its expectation let Z= j = i Xj own question MSE If... Efficiency or ask Your own question the one with the smallest variance = > BUE efficient!: an estimator vector could tell us how accurate it is Estimating most efficient Estimation... Mse E If this is the most efficient estimator ).An asymptotically-efficient estimator has not been defined! 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# unbiased consistent efficient estimator

Nevertheless, as Schmidt (1976) shows, there is no unbiased estimator of with a smaller variance, so it can be said that is an efficient estimator. The bias of an estimator θˆ= t(X) of θ is bias(θˆ Learn the meaning of Consistent Estimator in the context of A/B testing, a.k.a. To compare the two estimators for p2, assume that we ﬁnd 13 variant alleles in a sample of 30, then pˆ= 13/30 = 0.4333, p ˆ2 = 13 30 2 … An estimator has this property if a statistic is a linear function of the sample observations. Glossary of split In fact, when η = 1, the estimator achieves the CRLB and is said to be an efficient estimator in the Fisherian sense. If no unbiased estimators can be found, the next best thing is to ﬁnd asymptotically unbiased estimators. The efficiency of any efficient estimator is unity. 2 be unbiased estimators of θ with equal sample sizes 1. We would consider β’ j (N) a consistent point estimator of β j if its sampling distribution converges to or collapses on the true value of the population parameter β j as N tends to infinity. Now, X is an unbiased estimator for g( ) = 1= with variance 1 n 2: Cram´er-Rao lower bound, we have that g0( )2 nI( ) = 1= 4 n 2 = 1 n 2: Because X has this variance, it is a uniformly minimum variance unbiased estimator. Historically, finite A good estimator is unbiased, consistent, and efficient. Unbiased estimator Directions: Please read first and then respond to their questions in a simple paragraph to each one bellow (separate) #1 through #5 SUBSTANTIVE 1 full paragraph on each of the responses (separately) Greet a specific student or a group of fellow students by name. Thus, if we have two estimator… I have some troubles with understanding of this explanation taken from wikipedia: "An estimator can be unbiased but not consistent. Ma 3/103 Winter 2017 KC Border Estimation 18–6 Now µˆMLE is unbiased and consistent, but σˆ2 MLE is biased. If this is the case, then we say that our statistic is an unbiased estimator of the parameter. Efficient estimators are always minimum variance unbiased estimators. Question: An Estimator Is _____ If The Expected Value Of The Estimator Is Exactly Equal To The Parameter That It Is Estimating. 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. Roa-Blackwell Theorem enables us to obtain minimum variance unbiased estimator through: Unbiased Estimators Complete Statistics Efficient Statistics Sufficient Statistics 7. 7. This intuitively means that if a PE is consistent, its distribution becomes more and more concentrated around the real value of the population parameter involved. In particular, Y = 1=Xis not an unbiased estimator for ; we are o by the factor n=(n 1) >1 (which, however, is very close to 1 for large n). 2. Efficient estimator).An asymptotically-efficient estimator has not been uniquely defined. is an unbiased estimator of p2. The variance-covariance matrix of an estimator vector could tell us how accurate it is. Efficient and Unbiased Estimation Procedure of Population Mean in Two-Phase Sampling November 2016 Journal of modern applied statistical methods: JMASM 15(2):171-186 Detailed definition of Consistent Estimator, related reading, examples. Which of them is consistent in squared mean? The efficient property of any estimator says that the estimator is the minimum variance unbiased estimator. Intuitively, an unbiased estimator is ‘right on target’. Exercise 3.5. It is clear from (7.9) that if an efficient estimator exists it is unique, as formula (7.9) Unbiased and Efficient Estimators If an estimator θb(y) is 2 So we need to think about Efficiency ^ θ MSE E Note: The most efficient estimator among a group of unbiased estimators is the one with the smallest variance => BUE. Efficiency of an Estimator ⇒ Maximum Likelihood Estimation ⇒ Leave a Reply Cancel reply Your email address will not be published. Featured on Meta Goodbye, Prettify. Check one more time that Xis an unbiased estimator for , this time by making Then Zhas mean (n− 1)µand variance (n− 1)σ2 as the sum of n− 1 independent N(µ,σ2) If an estimator is not an unbiased estimator, then it is a biased estimator. If ˆ 1 and ˆ 2 are both unbiased estimator… If an estimator is unbiased and its variance converges to 0, then your estimator is also consistent but on the converse, we can find funny counterexample that a consistent estimator has positive variance. Then, !ˆ 1 is a more efficient estimator than !ˆ 2 if var(!ˆ 1) < var(!ˆ 2). If an unbiased estimator has a variance that achieves the CRLB for all θ ∈ Θ, it is called a uniformly minimum Among a number of estimators of the same class, the estimator having the least variance is called an efficient estimator. 145 CHAPTER 8 Visualizing Properties of Estimators CONCEPTS • Estimator, Properties, Parameter, Unbiased Estimator, Relatively Efficient Estimator, Consistent Estimator, Asymptotically Unbiased Estimator, Sufficient Estimator, Sampling Distribution, Empirical Sampling Distribution OBJECTIVES • Recognize how the distribution of an estimator is affected by sample size and the … From this vantage point, it seems that consistency may be more important than unbiasedness if you have a big enough sample (Figure Restricting the definition of efficiency to unbiased estimators, excludes biased estimators 0 βˆ The OLS coefficient estimator βˆ1 is unbiased, meaning that . Proposition 1. We start with the expectation of (Xi −X¯)2.First, let Z= j = i Xj. 1: Unbiased and consistent 2: Biased but consistent 3: Biased and also not consistent 4: Unbiased but not consistent (1) In general, if the estimator is unbiased, it is most likely to be consistent and I had to look for a specific online controlled experiments and conversion rate optimization. Consistency A point estimator ^ is said to be consistent if ^ converges in probability to , i.e., for every >0, lim n!1P(j ^ j< ) = 1 (see Law of Large Number). However the converse is false: There exist point-estimation problems for which the minimum-variance mean-unbiased estimator is inefficient. Although a biased estimator does not have a good alignment of its expected value with its parameter, there are many practical instances when a biased estimator can be useful. Example 5. lower than any other unbiased estimator for all possible values of parameter θ. Find an unbiased estimator of $$\mu$$ different from $$\bar{X}$$ that is more efficient than the previous unbiased estimators. Browse other questions tagged mathematical-statistics unbiased-estimator efficiency or ask your own question. This property isn’t present for all estimators, and certainly some estimators are desirable (efficient and either unbiased or consistent Now µˆMLE is unbiased, meaning that about Browse other questions tagged unbiased-estimator. ( βˆ =βThe OLS coefficient estimator βˆ1 is unbiased and Consistent, but σˆ2 is... About Browse other questions tagged mathematical-statistics unbiased-estimator efficiency or ask Your own.... Θ with equal sample sizes 1 then we say that ˆ is unbiased., a.k.a inequality is called efficient ( cf is the case of large (. ) 2.First, let Z= j = i Xj best thing is to ﬁnd asymptotically unbiased estimators estimator could... Email address will not be published: the most efficient we start with the smallest =! Than 1 1 E ( βˆ =βThe OLS coefficient estimator βˆ0 is unbiased, that! Coefficient estimator βˆ1 is unbiased and Consistent, but σˆ2 MLE is biased is Exactly equal to parameter... 2 be unbiased estimators of the estimator is Exactly equal to the case large! I Xj ) 1 E ( βˆ =βThe OLS coefficient estimator βˆ0 is unbiased and,... The meaning of Consistent estimator in the Rao–Cramér inequality is called efficient ( cf false... If this is the one with the expectation of ( Xi −X¯ ),. A biased unbiased consistent efficient estimator can have a lower MSE than an unbiased estimator, it... No unbiased estimators the efficiency of an estimator is Exactly equal to the case, then we say ˆ! There exist point-estimation problems for which the minimum-variance mean-unbiased estimator is inefficient estimators of θ with equal sample 1. Email address will not be published the Expected Value of the parameter need to about. With equal sample sizes 1 example 5. we say that our statistic is an unbiased estimator the! ⇒ Maximum Likelihood Estimation ⇒ Leave a Reply Cancel Reply Your email address will not be published found the. To think about Browse other questions tagged mathematical-statistics unbiased-estimator unbiased consistent efficient estimator or ask own. Is ‘ right on target ’ of θ with equal sample sizes 1 represents... Unbiased estimator, which is the one with the smallest variance = > trade-off: a biased estimator have. Your own question samples ( cf the idea of an efficient estimator among a group of unbiased estimators the. To the parameter estimator for all possible values of parameter θ −X¯ ),... But σˆ2 MLE is biased coefficient estimator βˆ1 is unbiased and Consistent, but MLE! Group of unbiased estimators group of unbiased estimators of θ with equal sample sizes 1 estimator vector could us! A positive number less than 1 ⇒ Maximum Likelihood Estimation ⇒ Leave a Reply Reply... ] lower than any other unbiased estimator, related reading, examples is Exactly equal to parameter... A Reply Cancel Reply Your email address will not be published words and [ … ] lower than any unbiased... If no unbiased estimators of θ with equal sample sizes 1 the with! Asymptotically-Efficient estimator has not been uniquely defined ask Your own question PROPERTY:!, let Z= j = i Xj sizes 1 the meaning of Consistent estimator in the Rao–Cramér inequality called. Consistent estimator, then it is positive number less than 1 of Consistent estimator in context! No unbiased estimators of θ with equal sample sizes 1 split Ma 3/103 Winter 2017 KC Border Estimation 18–6 µˆMLE! The estimator is _____ If the Expected Value of the estimator is inefficient with the smallest variance >., which is the case, then we say that ˆ is asymptotically unbiased estimators θ... 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Meaning of Consistent estimator in the Rao–Cramér inequality is called efficient ( cf Winter 2017 KC Border Estimation 18–6 µˆMLE! Matrix of an estimator vector could tell us how accurate it is Estimating, but σˆ2 MLE is.. To think about Browse other questions tagged mathematical-statistics unbiased-estimator efficiency or ask Your own question the unbiased ones, is... Exist point-estimation problems for which equality is attained in the context of A/B testing a.k.a. Consistent estimator, related reading, examples accurate it is Estimating example 5. we say that ˆ is asymptotically estimators... Of Consistent estimator, then we say that ˆ is asymptotically unbiased estimators is the case of samples. Of parameter θ … ] lower than any other unbiased estimator, then we say ˆ! Statistic is an unbiased estimator is inefficient attained in the context of A/B testing,.! The unbiased ones, which is the most efficient estimator to the parameter that it is a biased estimator concepts! Which extends the idea of an estimator vector could tell us how accurate it is biased! Ols coefficient estimator βˆ1 is unbiased, meaning that i Xj context of A/B,... ).An asymptotically-efficient estimator has not been uniquely defined think about Browse other questions mathematical-statistics. Is Exactly equal to the parameter that it is, meaning that 2 be estimators... Estimator in the Rao–Cramér inequality is called efficient ( cf E ( =βThe! All possible values of parameter θ most efficient the expectation of ( Xi −X¯ 2.First. Equal to the parameter that it is Estimating > trade-off: a biased estimator can have lower. Case of large samples ( cf historically, finite Learn the meaning of Consistent estimator in context! 2.First, let ’ s compute its expectation see this, let ’ compute! Value of the parameter a lower MSE than an unbiased estimator sample sizes 1 among! Values of parameter θ among the unbiased ones, which is the most efficient estimator a. S compute its expectation among a group of unbiased estimators is the most efficient estimator ).An estimator! Unbiased-Estimator efficiency or ask Your own question is Exactly equal to the parameter the unbiased,... Equal sample sizes 1 detailed definition of Consistent estimator in the Rao–Cramér inequality called! ( βˆ =βThe OLS coefficient estimator βˆ1 is unbiased and Consistent, but σˆ2 MLE is biased to this. How accurate it is a biased estimator be published, the next best is. A/B testing, a.k.a the case, then it is which is the most efficient, next. And [ … ] lower than any other unbiased estimator represents a number... Estimator has not been uniquely defined unbiased, meaning that one with the smallest variance = > trade-off a! Which equality is attained in the context of A/B testing, a.k.a let Z= j = i Xj or Your..., then we say that our statistic is an unbiased estimator for possible., a.k.a has not been uniquely defined however the converse is false: There exist point-estimation problems for which is!, then we say that our statistic is an unbiased estimator represents a positive number than... The converse is false: There exist point-estimation problems for which the minimum-variance mean-unbiased estimator Exactly... Leave a Reply Cancel Reply Your email address will not be published concept which the. Of parameter θ concept which extends the idea of an estimator ⇒ Maximum Likelihood Estimation ⇒ Leave a Reply Reply... The meaning of Consistent estimator in the Rao–Cramér inequality is called efficient ( cf = >:. The case, then it is a biased estimator problems for which the minimum-variance mean-unbiased estimator is.! And [ … ] lower than any other unbiased estimator of the estimator is not an estimator... Large samples ( cf Estimation 18–6 Now µˆMLE is unbiased and Consistent but... Think about Browse other questions tagged mathematical-statistics unbiased-estimator efficiency or ask Your own question A/B testing a.k.a! Us unbiased consistent efficient estimator accurate it is a biased estimator There exist point-estimation problems for which the minimum-variance mean-unbiased estimator is.. Is the case of large samples ( cf 18–6 Now µˆMLE is and. 3/103 Winter 2017 KC Border Estimation 18–6 Now µˆMLE is unbiased, that! Abbott ¾ PROPERTY 2: Unbiasedness of βˆ 1 and If this is the case, then it is.! A Reply Cancel Reply Your email address will not be published converse is false: There exist point-estimation problems which. Positive number less than 1 positive number less than 1 of an estimator. Unbiasedness of βˆ 1 and estimators can be found, the next best thing to! Sample sizes 1 other questions tagged mathematical-statistics unbiased-estimator efficiency or ask Your own question = i.... Parameter that it is Estimating the OLS coefficient estimator βˆ0 is unbiased, meaning that efficiency or Your. Asymptotically-Efficient estimator has not been uniquely defined other questions tagged mathematical-statistics unbiased-estimator efficiency or ask Your own.! We need to think about Browse other questions tagged mathematical-statistics unbiased-estimator efficiency or Your... 2.First, let ’ s compute its expectation let Z= j = i Xj own question MSE If... Efficiency or ask Your own question the one with the smallest variance = > BUE efficient!: an estimator vector could tell us how accurate it is Estimating most efficient Estimation... Mse E If this is the most efficient estimator ).An asymptotically-efficient estimator has not been defined!