Title: Shrinkage estimation of the mean of high-dimensional normal distribution
Authors: Ryota Yuasa - The University of Tokyo (Japan) [presenting]
Tatsuya Kubokawa - Faculty of Economics University of Tokyo (Japan)
Abstract: The problem of estimating the mean matrix of the multivariate normal distribution in high dimensional setting is addressed. Efron-Morris-type estimators with ridge-type inverse matrices are considered. The proposal to estimate optimal weights is based on the minimization of the risk function under a quadratic loss. The proposed estimators are derived by using Stein's identity. It is shown that the proposed estimators have minimaxity. Furthermore, by using Random Matrix Theory, it can be shown that proposed estimators are optimal from the viewpoint of the asymptotic minimization of the loss function when a prior distribution is assumed for the true mean. Numerical experiments are conducted to confirm the performance of the estimators, which are compared with Efron-Morris, James-Stein and singular value shrinkage type estimators. The proposed estimators provide better accuracy than the others, especially when both $n$ and $p$ are large.