A statistic whose expected value equals the population parameter is called what?

A statistic whose expected value equals the population parameter is called what?

• A. Unbiased Statistic
• B. Biased Statistic
• C. Efficient Statistic
• D. Consistent Statistic

Answer: (A)

An unbiased estimator is one whose expected value equals the population parameter. This means that if you could repeat the sampling process many times and compute the statistic each time, the average of those statistics would converge to the true parameter value. For example, the sample mean is an unbiased estimator of the population mean because E[ȳ] = μ. Biased would mean the average value of the statistic systematically deviates from the parameter. Efficient refers to having the smallest variance among unbiased estimators (when such a comparison is meaningful). Consistent means the statistic converges in probability to the parameter as the sample size grows.

An unbiased estimator is one whose expected value equals the population parameter. This means that if you could repeat the sampling process many times and compute the statistic each time, the average of those statistics would converge to the true parameter value. For example, the sample mean is an unbiased estimator of the population mean because E[ȳ] = μ.

Biased would mean the average value of the statistic systematically deviates from the parameter. Efficient refers to having the smallest variance among unbiased estimators (when such a comparison is meaningful). Consistent means the statistic converges in probability to the parameter as the sample size grows.