An estimator $\hat { \mu } _ { Y }$ of the population value $\mu _ { Y }$ is consistent if
A) $\hat { \mu } _ { Y } \stackrel { p } { \rightarrow } \mu _ { Y } .$
B) its mean square error is the smallest possible.
C) Y is normally distributed.
D) $\bar { Y } \stackrel { p } { \rightarrow } 0$

Question

An estimator $\hat { \mu } _ { Y }$ of the population value $\mu _ { Y }$ is consistent if
A) $\hat { \mu } _ { Y } \stackrel { p } { \rightarrow } \mu _ { Y } .$
B) its mean square error is the smallest possible.
C)  Y  is normally distributed.
D) $\bar { Y } \stackrel { p } { \rightarrow } 0$

Quizplus · Accepted Answer

An estimator is consistent if it converges in probability to the true parameter value as the sample size increases, which is described by $\hat { \mu } _ { Y } \stackrel { p } { \rightarrow } \mu _ { Y }$.

An Estimator μ^Y\hat { \mu } _ { Y }μ^​Y​ Of the Population Value

An Estimator $\hat { \mu } _ { Y }$ Of the Population Value