Among all unbiased estimators that are weighted averages of Y1,... ,Yn ,is
A)the only consistent estimator of µY.
B)the most efficient estimator of µY.
C)a number which,by definition,cannot have a variance.
D)the most unbiased estimator of µY.

Question

Among all unbiased estimators that are weighted averages of Y1,... ,Yn  ,is
A)the only consistent estimator of µY. 
B)the most efficient estimator of µY. 
C)a number which,by definition,cannot have a variance. 
D)the most unbiased estimator of µY.

Quizplus · Accepted Answer

The most efficient estimator is the one with the smallest variance. Since all unbiased estimators that are weighted averages of Y1,... ,Yn have the same bias, the one with the smallest variance is the most efficient. Therefore, the answer is B.

Among All Unbiased Estimators That Are Weighted Averages of Y1