In this paper, we consider the problems of estimating the univariate and multivariate components of variance in elliptically contoured distribution (ECD) model in a decision-theoretic setup. Empirical Bayes or generalized Bayes estimators and several other positive or nonnegative (definite)...

One of the surprising decision-theoretic result Charles Stein discovered is the inadmissibility of the uniformly minimum variance unbiased estimator (UMVUE) of the variance of a normal distribution with an unknown mean. Some methods for deriving estimators better than the UMVUE were given by...

In this paper, we consider the problem of estimating the regression parameters in a multiple linear regression model with design matrix A when the multicollinearity is present. Minimax empirical Bayes estimators are proposed under the assumption of normality and loss function (ƒÂ-s)t (At A)2...

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...

In a balanced one-way model with random effects, the simultaneous estimation of the variance components are considered under the intrinsic Kullback-Leibler loss function. The uniformly minimum variance unbiased (UMVU) or ANOVA estimators are known to have a drawback of taking negative values....

When a location parameter is restricted to a bounded interval, the paper addresses the issue of deriving estimators improving on the best location equivariant (or Pitman) estimator under the squared error loss. A class of improved estimators is constructed, and it is verified that the Bayes...

Consider the problem of testing the linear hypothesis on regression coefficients in the nested error regression model. The standard F-test statistic based on the ordinary least squares (OLS) estimator has the serious shortcoming that its type I error rates (sizes) are much larger than nominal...

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 the estimation of a mean vector of a multivariate normal distribution, the paper obtains conditions for minimaxity of hierarchical Bayes estimators against hierarchical prior distributions where three types of second stage priors are treated. Conditions for admissibility and inadmissibility...

The estimation of the precision matrix of the Wishart distribution is one of classical problems studied in a decision-theoretic framework and is related to estimation of mean and covariance matrices of a multivariate normal distribution. This paper revisits the estimation problem of the...