<p>In this article, we propose tests for covariance matrices of high dimension with fewer observations than the dimension for a general class of distributions with positive definite covariance matrices. In one-sample case, tests are proposed for sphericity and for testing the hypothesis that the...</p>

We consider minimax shrinkage estimation of a location vector of a spherically symmetric distribution under a loss function which is a concave function of the usual squared error loss. In particular for distributions which are scale mixtures of normals (and somewhat more generally), and for...

This paper is concerned with estimation of a predictive density with parametric constraints under Kullback-Leibler loss. When an invariance structure is embed- ded in the problem, general and unied conditions for the minimaxity of the best equivariant predictive density estimator are derived....

Our investigation concerns the estimation of predictive densities and a study of effiency as measured by the frequentist risk of such predictive densities with integrated L2 and L1 losses. Our findings relate to a p-variate spherically symmetric observable X ∼ px (||x -μ||2) and the...

In this paper, we suggest the new variable selection procedure, called MEC, for linear discriminant rule in the high-dimensional setup. MEC is derived as a second-order unbiased estimator of the misclassication error probability of the lin- ear discriminant rule. It is shown that MEC not only...

The paper concerns small-area estimation in the heteroscedastic nested error regression (HNER) model which assumes that the within-area variances are different among areas. Although HNER is useful for analyzing data where the within-area variation changes from area to area, it is difficult to...

This paper is concerned with the prediction of the conditional mean which involves the fixed and random effects based on the natural exponential family with a quadratic variance function. The best predictor is interpreted as the Bayes estimator in the Bayesian context, and the empirical Bayes...

The problem of estimating a covariance matrix in multivariate linear regression models is addressed in a decision-theoretic framework. Although a standard loss function is the Stein loss, it is not available in the case of a high dimension. In this paper, a new type of a quadratic loss function,...

　　 This paper addresses the problem of estimating the normal mean matrix with an unknown covariance matrix. Motivated by an empirical Bayes method, we suggest a unied form of the Efron-Morris type estimators based on the Moore-Penrose inverse. This form not only can be dened for...

In this paper, we consider the problem of selecting explanatory variables of fixed effects in linear mixed models under covariate shift, which is the situation that the values of covariates in the predictive model are different from those in the observed model. We construct a variable selection...