A consistent estimator is one whose estimates converge to the true parameter as sample size grows.

A consistent estimator is one whose estimates converge to the true parameter as sample size grows.

• A. Converges to the true parameter as n grows
• B. Becomes more biased with larger samples
• C. Ignores the sample size
• D. Is always unbiased

Answer: (A)

Consistency means the estimator becomes arbitrarily close to the true parameter as the sample size grows. In probability terms, it converges in probability to the parameter as n increases. That exact idea is captured by the statement that the estimates converge to the true parameter as the sample size grows. A familiar example is the sample mean of independent observations with a finite mean: by the Law of Large Numbers, the sample mean converges in probability to the population mean as n grows. This reflects consistency, and while the sample mean is unbiased in many common cases, the essential point is that more data should lead to more accurate estimates. The other options conflict with this concept. An estimator that becomes more biased as n increases would not settle near the true parameter. If an estimator ignores the sample size, its accuracy wouldn’t improve as more data are collected. And being always unbiased is not required for consistency; you can have biased estimators that are still consistent because their bias vanishes as n grows.

Consistency means the estimator becomes arbitrarily close to the true parameter as the sample size grows. In probability terms, it converges in probability to the parameter as n increases. That exact idea is captured by the statement that the estimates converge to the true parameter as the sample size grows.

A familiar example is the sample mean of independent observations with a finite mean: by the Law of Large Numbers, the sample mean converges in probability to the population mean as n grows. This reflects consistency, and while the sample mean is unbiased in many common cases, the essential point is that more data should lead to more accurate estimates.

The other options conflict with this concept. An estimator that becomes more biased as n increases would not settle near the true parameter. If an estimator ignores the sample size, its accuracy wouldn’t improve as more data are collected. And being always unbiased is not required for consistency; you can have biased estimators that are still consistent because their bias vanishes as n grows.