When choosing between two unbiased estimators of the same parameter, the preferred estimator is:
A) the one that is most unbiased.
B) the one with the smaller variance.
C) the one that has an expected value equal to the parameter.
D) Either estimator is fine, as both are unbiased.

Question

Quizplus · Accepted Answer

While both estimators are unbiased, the preferred estimator is the one with the smaller variance. A smaller variance indicates that the estimator is more precise and will produce estimates closer to the true value of the parameter. In contrast, an estimator with a larger variance will produce estimates that are more variable and may be further from the true value of the parameter. Therefore, when choosing between two unbiased estimators, we should prefer the one with the smaller variance.

When Choosing Between Two Unbiased Estimators of the Same Parameter