If _j, an unbiased estimator of _j, is consistent, then the: A)distribution of _j becomes more and more loosely distributed around _j as the sample size grows. B)distribution of _j becomes more and more tightly distributed around _j as the sample size grows. C)distribution of _j tends toward a standard normal distribution as the sample size grows. D)distribution of _j remains unaffected as the sample size grows.

Question

Quizplus · Accepted Answer

Consistency means that as the sample size increases, the estimator converges to the true parameter value. In other words, the distribution of the estimator becomes more and more concentrated around the true value as the sample size grows. Therefore, choice B is correct. Choice A describes a situation of increasing variance, not concentration. Choice C describes convergence to a standard distribution, which may not be applicable in all cases. Choice D implies that the sample size has no effect on the distribution of the estimator, which is untrue for consistent estimators.

If j, an Unbiased Estimator of j, Is

If _j, an Unbiased Estimator of _j, Is