Improved estimators of common variance of p-populations when Kurtosis is known

Abstract

The pooled variance of p samples presumed to have been obtained from p populations having common variance σ², $S^2_{\rm pooled}$ has invariably been adopted as the default estimator for σ². In this paper, alternative estimators of the common population variance are developed. These estimators are biased and have lower mean-squared error values than $S^2_{\rm pooled}$ . The comparative merit of these estimators over the unbiased estimator is explored using relative efficiency (a ratio of mean-squared error values).