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...

This paper addresses the issue of constructing a confidence interval of a small area mean in a random effect or mixed effects linear model. A crude confidence interval based on the empirical Bayes method has the drawback that its coverage probability is much less than a nominal confidence...

Random effects and restriction of parameters are important concepts in constructing statistical models based on small samples: Restricting the parameter spaces to subspaces constrained by inequalities or equalities yields pooling the data to get stablized estimators, and incorporating the random...

Linear mixed models (LMM) and the best linear unbiased predictor (BLUP) have received considerable attention in recent years from both theoretical and practical aspects. This article reviews the theory of LMM and illustrates how useful LMM and BLUP are through an example of the small area...

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...

This paper is concerned with estimation of the restricted parameters in location and/or scale families from a decision-theoretic point of view. A simple method is provided to show the minimaxity of the best equivariant and unrestricted estimators. This is based on a modification of the known...

The estimation of a mean of a normal distribution with an unknown variance is addressed under the restriction that the coefficient of variation is within a bounded interval. The paper constructs a class of estimators improving on the best location-scale equivariant estimator of the mean. It is...

The problem of estimating covariance and precision matrices of multivariate normal distributions is addressed when both the sample size and the dimension of variables are large. The estimation of the precision matrix is important in various statistical inference including the Fisher linear...