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Title: Shrinkage estimation of the mean of high-dimensional normal distribution Authors:  Ryota Yuasa - The Institute of Statistical Mathematics (Japan) [presenting]
Tatsuya Kubokawa - Faculty of Economics University of Tokyo (Japan)
Abstract: The problem of the estimation of the mean matrix of the multivariate normal distribution in high dimensional setting have been addressed. The Efron-Morris-type estimators with ridge-type inverse matrices are considered, and the proposal for estimation of optimal weights is estimator based on minimizing the risk function under the quadratic loss. Two approaches were considered, one is a method using random matrix theory, and the other is a method using Stein's identity. By considering these two methods, it can be seen that the estimators derived by the method using Stein's identity have optimality from the viewpoint of asymptotic minimization of the loss function when the prior distribution is assumed to be the true mean. It was also shown that under some assumptions, the proposed estimator has minimaxity. Numerical experiments are conducted to confirm the effect of the choice of ridge parameter on the estimation. The proposed estimators were compared with Efron-Morris estimator and James-Stein estimator. The proposed estimators provide better estimation accuracy than the Efron-Morris estimator, especially when both n and p are large, than the other estimators to be compared.