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...

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...

Sample survey data can be used to derive a reliable estimate of a total mean for a large area. When the same data are used to estimate means of small areas like city, county or town belonging to the large area, the usual direct estimators like the sample mean have unacceptably large standard...

The Box-Cox transformation is applied to linear mixed models for analyzing positive and clustered data. The problem is that the maximum likelihood estimator of the transformation parameter is not consistent. To fix it, we suggest a simple and consistent estimator for the transformation parameter...

The problem of estimating large covariance matrices with use of factor models is addressed when both the sample size and the dimension of covariance matrix tend to innity. In this paper, we consider a general class of weighted estimators which includes (i) linear combinations of the sample...