The problem of estimation of the ratio of variance components is considered from the invariance point of view. This approach actually paves the way for proving the inadmissibility of the optimal estimator developed by Loh (1986). A class of shrinkage estimators is also proposed. These estimators...

We consider the problem of estimating a p-dimensional vector [mu]1 based on independent variables X1, X2, and U, where X1 is Np([mu]1, [sigma]2[Sigma]1), X2 is Np([mu]2, [sigma]2[Sigma]2), and U is [sigma]2[chi]2n ([Sigma]1 and [Sigma]2 are known). A family of minimax estimators is proposed....

Let X1,...,Xn (n1, p1) be independently and identically distributed normal p-vectors with mean [mu] and covariance matrix ([mu]'[mu]/C2)I, where the coefficient of variation C is known. The authors have obtained the best equivariant estimator of [mu] under the loss function...

Let S: p - p have a nonsingular Wishart distribution with unknown matrix [Sigma] and n degrees of freedom, n = p. For estimating [Sigma], a family of minimax estimators, with respect to the entropy loss, is presented. These estimators are of the form (S) = R[Phi](L) Rt, where R is orthogonal, L...

Let X1, ..., Xn (n p 2) be independently and identically distributed p-dimensional normal random vectors with mean vector [mu] and positive definite covariance matrix [Sigma] and let [Sigma] and . be partioned as1 p-1 1 p-1. We derive here the best equivariant estimators of the regression...