How is the consistency of estimators defined?
A)An estimator is consistent if its expected value equals the estimated population parameter.
B)A consistent estimator approaches the estimated population parameter as the sample size grows larger.
C)An estimator is consistent if it always gives the correct value of the estimated population parameter.
D)An unbiased estimator is consistent if its standard error is lower than that of other estimators of the estimated population parameter.

Question

Quizplus · Accepted Answer

Consistency of an estimator is defined as the property that it approaches the true population parameter value as the sample size grows larger. Therefore, choice B is correct. Choice A is incorrect because an estimator can be unbiased but not consistent. Choice C is incorrect because no estimator can always give the correct value, as there is always some sampling error. Choice D is incorrect because being unbiased does not necessarily imply consistency, and the standard error is only one measure of the precision of an estimator.

How Is the Consistency of Estimators Defined