It is well known that the uniformly minimum variance unbiased (UMVU) estimators of the risk and the mean squared error (MSE) matrix proposed in the literature for Stein estimators can take negative values with positive probability. In this paper, improved truncated estimators of the risk, risk...

The multivariate mixed linear model or multivariate components of variance model with equal replications is considered. The paper addresses the problem of predicting the sum of the regression mean and the random effects. When the feasible best linear unbiased predictors or empirical Bayes...

This paper derives extended versions of 'Stein' and 'Haff' or more appropriately 'Stein-Haff' identities for elliptically contoured distribution (ECD) models. These identities are then used to establish the robustness of shrinkage estimators for the regression parameters in the multivariate...

In this paper, we consider a multivariate one-way random effect model with equal replications. We propose non-negative definite estimators for 'between' and 'within' components of variance. Under the Stein loss function/Kullback-Leibler distance function, these estimators are shown to be better...

In this paper we consider the problem of estimating the matrix of regression coefficients in a multivariate linear regression model in which the design matrix is near singular. Under the assumption of normality, we propose empirical Bayes ridge regression estimators with three types of shrinkage...

In microarray experiments, the dimension p of the data is very large but there are only few observations N on the subjects/patients. In this article, the problem of classifying a subject into one of the two groups, when p is large, is considered. Three procedures based on Moore-Penrose inverse...

The problem of estimating the common regression coefficients is addressed in this paper for two regression equations with possibly different error variances. The feasible generalized least squares (FGLS) estimators have been believed to be admissible within the class of unbiased estimators. It...

For Wishart density functions, the risk dominance problems of moment estimators, maximum likelihood estimators (MLEs), James-Stein type minimax estimators and their improved estimators of covariance matrices under the Kullback-Leibler loss function have been well studied in the literature....

Consider the problem of testing the linear hypothesis on the regression coefficients in the Fay-Herriot model which has been used in the small area problem. Since this model involves the random effects, a test based on the generalized least squares estimator, called the GLS test, depends on the...

In the estimation of a multivariate normal mean, it is shown that the problem of deriving shrinkage estimators improving on the maximum likelihood estimator can be reduced to that of solving an integral inequality. The integral inequality not only provides a more general condition than a...