Two Stage Estimation of the Variance of a Normal Population

Abstract

Given a normally distributed random sample with known mean and unknown variance σ², two stage estimation method is used to estimate σ², utilizing some available prior information. The mean square errors (MSE) of the new estimators are compared to that of the usual estimator of σ², namely, the sample variance. It turns out that, when the actual value of σ² is not too inconsistent with the prior information, the new estimators are much better than the usual estimator of σ².