Exam MAS-I Practice Question 61

Study guide: Exam MAS-I

Let $W$ be an unbiased estimator of a parameter $\theta$ , computed from a random sample $X_1, \ldots, X_n$ , and let $T$ be a statistic computed from the same sample.

Determine which of the following statements are true.

I. If $T$ is sufficient for $\theta$ , then $E[W \mid T]$ is unbiased for $\theta$ and its variance is no larger than $\text{Var}(W)$ , whatever the value of $\theta$ .
II. If $T$ is not sufficient for $\theta$ , then $E[W \mid T]$ can depend on $\theta$ , in which case it cannot be computed from the data and is not an estimator.
III. If $T$ is sufficient but not complete, then $E[W \mid T]$ is still guaranteed to be the minimum variance unbiased estimator of $\theta$ , whichever unbiased $W$ is used.
A) I only
B) I and II only
C) I and III only
D) II and III only
E) The answer is not given by (A), (B), (C), or (D)

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Concepts tested

Rao-Blackwell Theorem
Sufficient Statistic
Unbiasedness
Minimum Variance

Exam MAS-I Practice Question 61

Concepts tested

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