In this article, Stein-Haff identity is established for a singular Wishart distribution with a positive definite mean matrix but with the dimension larger than the degrees of freedom. This identity is then used to obtain estimators of the precision matrix improving on the estimator based on the...

In this paper, we consider the prediction problem in multiple linear regression model in which the number of predictor variables, p, is extremely large compared to the number of available observations, n. The least squares predictor based on a generalized inverse is not efficient. It is shown...

We propose an information criterion which measures the prediction risk of the predictive density based on the Bayesian marginal likelihood from a frequentist point of view. We derive the criteria for selecting variables in linear regression models by putting the prior on the regression...

In this article, we consider the problem of testing the equality of mean vectors of dimension p of several groups with a common unknown non-singular covariance matrix Σ, based on N independent observation vectors where N may be less than the dimension p. This problem, known in the literature as...

We consider two hypothesis testing problems with N independent observations on a single m-vector, when mN, and the N observations on the random m-vector are independently and identically distributed as multivariate normal with mean vector μ and covariance matrix Σ, both unknown. In the first...

In this paper we propose a test for testing the equality of the mean vectors of two groups with unequal covariance matrices based on N1 and N2 independently distributed p-dimensional observation vectors. It will be assumed that N1 observation vectors from the first group are normally distributed...

<p>In this article, we propose tests for covariance matrices of high dimension with fewer observations than the dimension for a general class of distributions with positive definite covariance matrices. In one-sample case, tests are proposed for sphericity and for testing the hypothesis that the...</p>

The paper addresses the problem of selecting variables in the two-stage sampling models characterized as a linear mixed model. We obtain the Empirical Bayes Information Criterion (EBIC) using a prior distribution on regression coefficients with an unknown hyper-parameter. It is shown that EBIC...