On empirical Bayes estimation of multivariate regression coefficient

• Main Authors: R. J. Karunamuni, L. Wei
• Format: Article
• Language: English
• Published: Hindawi Limited 2006-01-01
• Series: International Journal of Mathematics and Mathematical Sciences
• Online Access: http://dx.doi.org/10.1155/IJMMS/2006/51695

We investigate the empirical Bayes estimation problem of multivariate regression coefficients under squared error loss function. In particular, we consider the regression model Y=Xβ+ε, where Y is an m-vector of observations, X is a known m×k matrix, β is an unknown k-vector, and ε is an m-vector of unobservable random variables. The problem is squared error loss estimation of β based on some “previous” data Y1,…,Yn as well as the “current” data vector Y when β is distributed according to some unknown distribution G, where Yi satisfies Yi=Xβi+εi, i=1,…,n. We construct a new empirical Bayes estimator of β when εi∼N(0,σ2Im), i=1,…,n. The performance of the proposed empirical Bayes estimator is measured using the mean squared error. The rates of convergence of the mean squared error are obtained.