For a multivariate normal distribution with unknown mean vector and unknown dispersion matrix, a sequential procedure for estimating the unknown mean vector is suggested. The procedure is shown to be asymptotically "risk efficient" in the sense of Starr (Ann. Math. Statist. (1966), 1173-1185),...

We consider the problem of estimation of [mu]1 when it is suspected that [mu]1 [approximate] [mu]2 based on independent samples from Np([mu]1, [sigma]2V1) and Np([mu]2, [sigma]2V2). We assume V1, V2 known but [sigma]2 unknown. First, the EB estimator is derived and its Bayesian and frequentist...

In the class of multivariate exponential power distributions, we derive LBI (locally best invariant) tests for normality in the two cases: (i) mean vector [mu] is known and (ii) [mu] is unknown. In the case (i), the null and nonnull asymptotic distributions of the test statistic are derived. In...

Let Rn-p, (n), Gl(p) and +(p) denote respectively the set of n-p matrices, the set of n-n orthogonal matrices, the set of p-p nonsingular matrices and the set of p - p positive definite matrices. In this paper, it is first shown that a bijective and bimeasurable transformation (BBT) g on...

In this paper, first we make a maximal extension of the well-known Gauss-Markov Theorem (GMT) in its linear framework. In particular, the maximal class of distributions of error term for which the GMT holds is derived. Second, we establish a nonlinear version of the maximal GMT and describe some...

This paper considers the problem of estimating the coefficient matrix B: m - p in a normal multivariate regression model under the risk matrix : m - m and obtains classes of minimax estimators for Baranchik type, Strawderman type, Efron-Morris type, and Stein type estimators.

In this paper, the authors propose a locally most powerful invariant test for the equality of means in the presence of covariate variables. Also the null and nonnull distributions associated with the above test are developed. This problem arises in covariate discriminant analysis and has been...

In the GMANOVA model or equivalent growth curve model, shrinkage effects on the MLE (maximum likelihood estimator) are considered under an invariant risk matrix. We first study the fundamental structure of the problem through which we decompose the estimation problem into some conditional...

Sufficient conditions are given that certain statistics have a common distribution under a wide class of underlying distributions. Invariance methods are the primary technical tool in establishing the theoretical results. These results are applied to MANOVA problems, problems involving canonical...

In this paper, the authors considered various procedures for testing for the independence of two multivariate regression equations with different design matrices. Asymptotic null distributions as well as nonnull distributions under local alternatives of the test statistics associated with the...