A0841
Title: Weighted shrinkage estimators of normal mean matrices
Authors: Ryota Yuasa - The Institute of Statistical Mathematics (Japan) [presenting]
Tatsuya Kubokawa - Faculty of Economics University of Tokyo (Japan)
Abstract: In the estimation of the mean matrix in a multivariate normal distribution, the Efron-Morris estimator and the James-Stein estimator are two well-known minimax procedures, where the former is matricial shrinkage and the latter is scalar shrinkage. The methods for combining the two estimators with random weight functions are addressed. For deriving weight functions, we suggest the two methods. One is the minimization of a part of the unbiased estimator of the risk function, and the other is the empirical Bayes approach. The resulting weights are related to statistics for testing the sphericity of a covariance matrix. The resulting weighted shrinkage estimators are minimax. We also consider the case of an unknown covariance matrix. Numerical experiments are conducted to confirm the theoretical findings.
