Knowing that an estimator is unbiased only assures us that its expected value equals the parameter,but it does not tell us how close the estimator is to the parameter.

Question

Quizplus · Accepted Answer

Unbiasedness only ensures that, on average, the estimator is "correct" and does not have any systematic bias. It is possible for an unbiased estimator to have high variance or be very far off from the true value in some cases. Therefore, unbiasedness does not necessarily imply closeness to the parameter.

Knowing That an Estimator Is Unbiased Only Assures Us That