It is possible for an estimator of ${ } ^ { \mu } \gamma$ to be inconsistent while A)converging in probability to ${ } ^ { \mu } \gamma$ B)S_n $\stackrel { p } { \rightarrow }$ ${ } ^ { \mu } \gamma$ C)unbiased. D)Pr $\left[ \left| S _ { n } - \mu _ { Y } \right| \geq \delta \right]$ ? 0.

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Quizplus · Accepted Answer

An estimator can be unbiased but still inconsistent if its variance does not decrease to zero as the sample size increases. Being unbiased means the expected value of the estimator equals the parameter being estimated, but consistency requires that the estimator converges in probability to the parameter as the sample size increases to infinity.

It Is Possible for an Estimator Of μγ{ } ^ { \mu } \gammaμγ

It Is Possible for an Estimator Of ${ } ^ { \mu } \gamma$