Improved estimation of kurtosis parameters for two multivariate populations

Abstract

Improved estimators for the kurtosis parameters of two multivariate populations are developed under the assumption that they are equal. Shrinkage and preliminary test estimators are proposed and their asymptotic properties are presented analytically and numerically. Comparisons of the suggested estimators are made on the basis of their asymptotic distributional biases and asymptotic quadratic risks. It is observed that the suggested estimators perform better than the estimator based on the sample data only in a wider range of parametric space.