Bayes invariant quadratic estimation in general linear regression models

Abstract

In the paper the general linear regression model E( y )= Xβ , Cov( y)= Σ k i=1 σ 2 i V i ; V i ≥0, i=1,2,…, k−1, V k = I , is considered. For this model explicit formulae for the Bayes invariant quadratic unbiased estimators and the Bayes invariant quadratic estimators are given. These estimators are expressed in terms of a base of a Jordan algebra generated by MV 1 M , MV 2 M ,…, MV k−1 M , M , where M is the orthogonal projector on the null space of X ′. Two-way classification random models corresponding to orthogonal and partially balanced block designs are considered as examples.