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

The pooled variance of p samples presumed to have been obtained from p populations having common variance σ2, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S^2_{\rm pooled}$$\end{document} 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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S^2_{\rm pooled}$$\end{document} . The comparative merit of these estimators over the unbiased estimator is explored using relative efficiency (a ratio of mean-squared error values).