Consistency for the sample average $\bar { Y }$ can be defined as follows, with the exception of
A) $\bar { Y }$ converges in probability to $\mu_y$
B) $\bar { Y }$ has the smallest variance of all estimators.
C) $\bar { Y } \xrightarrow{P} \mu _ { y}$
D)the probability of $\bar { Y }$ being in the range $\mu_y$ ± c becomes arbitrarily close to one as n increases for any constant c 0.

Question

Consistency for the sample average $\bar { Y }$ can be defined as follows, with the exception of
A) $\bar { Y }$ converges in probability to $\mu_y$
B) $\bar { Y }$ has the smallest variance of all estimators.
C) $\bar { Y } \xrightarrow{P} \mu _ { y}$
D)the probability of $\bar { Y }$ being in the range $\mu_y$ ± c becomes arbitrarily close to one as n increases for any constant c > 0.

Quizplus · Accepted Answer

Consistency refers to the property that the sample average converges in probability to the true mean as the sample size increases. It does not imply having the smallest variance among all estimators.

Consistency for the Sample Average Yˉ\bar { Y }Yˉ Can Be Defined as Follows, with the Exception of A)

Consistency for the Sample Average $\bar { Y }$ Can Be Defined as Follows, with the Exception of
A)