Developments in Decision-Theoretic Variance Estimation

Abstract

This article traces the history of the problem of estimating the variance, $\sigma^2$, based on a random sample from a normal distribution with mean $\mu$ unknown. Considered are both the point estimation and confidence interval cases. We see that improvement over both usual estimators follows a remarkably parallel development and stemmed from the innovative ideas presented in Stein (1964). We examine developments through the most recent dealing with improved confidence intervals and conditional evaluations of interval estimators.