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...

Simultaneous lower bounds (SLB) for the isotonic contrasts in normal means are obtained. In particular a SLB for the range is given. These SLBs are obtained from the one-sided max t test. It is then generalized to obtain simultaneous upper bounds for the responses at lower levels. Under the...

In this paper, we consider a test for the mean vector of independent and identically distributed multivariate normal random vectors where the dimension p is larger than or equal to the number of observations N. This test is invariant under scalar transformations of each component of the random...

The Akaike information criterion (AIC) has been used very successfully in the literature in model selection for small number of parameters pand large number of observations N. The cases when pis large and close to N or when pN have not been considered in the literature. In fact, when pis large...

Likelihood ratio tests for detecting a single outlier in multivariate linear models are considered, where an observation is called an outlier if there has been a shift in the mean. The test statistics are the maximum of n nonindependent statistics, where n is the number of observations. Relevant...

In this article, the 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...

In this article, we consider the problem of testing a linear hypothesis in a multivariate linear regression model which includes the case of testing the equality of mean vectors of several multivariate normal populations with common covariance matrix [Sigma], the so-called multivariate analysis...

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...

In this paper, we consider the problem of selecting the variables of the fixed effects in the linear mixed models where the random effects are present and the observation vectors have been obtained from many clusters. As the variable selection procedure, we here use the Akaike Information...