Consistency for the sample average can be defined as follows,with the exception of
A) converges in probability to .
B) has the smallest variance of all estimators.
C) .
D)the probability of being in the range ± c becomes arbitrarily close to one as n increases for any constant c 0.

Question

Consistency for the sample average  can be defined as follows,with the exception of
A) converges in probability to . 
B) has the smallest variance of all estimators. 
C) . 
D)the probability of being in the range ± c becomes arbitrarily close to one as n increases for any constant c > 0.

Quizplus · Accepted Answer

Consistency requires that the estimator converges in probability to the true value. Option A talks about convergence, but the changed last four digits of the identifier make it a different estimator altogether. Option C does not provide any information related to convergence. Option D is related to the concept of convergence, but it talks about the probability of the estimator being in a range, not about convergence towards the true value. Option B, on the other hand, states that the given estimator has the smallest variance of all estimators, which is a desirable property for estimators but not necessarily related to consistency. However, since options A, C, and D are incorrect, option B is the best choice.

Consistency for the Sample Average Can Be Defined as Follows,with