BAYES INVARIANT QUADRATIC ESTIMATION IN GENERAL LINEAR-REGRESSION MODELS

In the paper the general linear regression model E(y) = X-beta, Cov(y) = SIGMA(i=1)k sigma(i)2V(i); V(i) greater-than-or-equal-to 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 MV1M, MV2M,...,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.