Empirical bayes minimax estimators of matrix normal means for arbitrary quadratic loss and unknown covariance matrix

Gwowen Shieh*

*此作品的通信作者

研究成果: Article同行評審

4 引文 斯高帕斯(Scopus)

摘要

Let X = (X1,…, XK), where Xi are mutually independent p-variate (K > p+1) normal vectors with unknown means θiand unknown positive definite variance-covariance matrix V. Assume the statistic V is available for estimating V, where V has a Wishart distribution WP(n, V)/(n+p+1), n> p+1, and is independent of X. It is desired to estimate θ = (θ1,…,θK) under the quadratic loss LQ*(θ, θ) = tr{(θ - θ)1Q*(θ - θ)}, where Q* = V-1/2QV-1/2, V =V1/2V1/2, and Q is a known positive definite matrix chosen by the researcher. The LQ* loss includes the widely used loss L(θ, θ) = tr{(θ - θ)1V-1(θ - θ)} as a special case. It is shown that under some specifications of τ(V,S), a symmetric pxp matrix, the proposed empirical Bayes estimator (Ip - (VS-1 τ(V, S))X dominates the maximum likelihood estimator X and is minimax under the LQ* loss. Unlike the previous work on the estimation of vector normal means under quadratic losses with a weight matrix Q, the proposed empirical Bayes minimax estimators are structurally free of Q and the minimaxity holds for a class of quadratic loss functions LQ*. The simulated risks of several competing EB estimators are considered, and the risk improvement of these estimators over the sample mean is calculated.

原文English
頁(從 - 到)317-342
頁數26
期刊Statistics and Risk Modeling
11
發行號4
DOIs
出版狀態Published - 4月 1993

指紋

深入研究「Empirical bayes minimax estimators of matrix normal means for arbitrary quadratic loss and unknown covariance matrix」主題。共同形成了獨特的指紋。

引用此