The Asymptotic Expansion of the Stein Estimator for the Matrix Case with Covariance Matrix sigma Hyperon Unknown

摘要

The method used to determine the existence of estimators which dominate the maximum likelihood estimators for the problem of simultaneously estimating the means of three or more random variables was extended from the vector case to the matrix case. The asymptotic distribution, mean and variance of the Stein estimator was derived as well as that of the quadratic loss function for the matrix case with covariance matrix Sigma unknown.