On empirical Bayes estimation of multivariate regression coefficient

R. J. Karunamuni and L. Wei

International Journal of Mathematics and Mathematical Sciences, 2006, vol. 2006, 1-18

Abstract:

We investigate the empirical Bayes estimation problem of multivariate regression coefficients under squared error loss function. In particular, we consider the regression model Y = X β + 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 Y 1 , … , Y n as well as the “current†data vector Y when β is distributed according to some unknown distribution G , where Y i satisfies Y i = X β i + ε i , i = 1 , … , n . We construct a new empirical Bayes estimator of β when ε i ∼ N ( 0 , σ 2 I m ) , 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.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:051695

DOI: 10.1155/IJMMS/2006/51695

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