Which term describes an estimator that is unbiased?

Which term describes an estimator that is unbiased?

• A. Unbiased
• B. Biased
• C. Consistent
• D. Inconsistent

Answer: (A)

An unbiased estimator is one whose expected value equals the true parameter it’s estimating. In other words, if you could repeat the sampling process many times and compute the estimator each time, the average of those estimates would equal the parameter. This is why the term describing such an estimator is unbiased—the bias is defined as E[estimator] − θ, which would be zero. Different from this, consistency concerns what happens as you collect more data. An estimator is consistent if it converges in probability to the true parameter as sample size grows. An estimator can be unbiased for finite samples but not necessarily consistent (and vice versa, though many common estimators are both).

An unbiased estimator is one whose expected value equals the true parameter it’s estimating. In other words, if you could repeat the sampling process many times and compute the estimator each time, the average of those estimates would equal the parameter. This is why the term describing such an estimator is unbiased—the bias is defined as E[estimator] − θ, which would be zero.

Different from this, consistency concerns what happens as you collect more data. An estimator is consistent if it converges in probability to the true parameter as sample size grows. An estimator can be unbiased for finite samples but not necessarily consistent (and vice versa, though many common estimators are both).