<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>

The problem of estimating the large covariance matrix of both normal and non-normal distributions is addressed. In convex combinations of the sample covariance　matrix and the identity matrix multiplied by a scalor statistic, we suggest a new　estimator of the optimal weight based on...

We propose an information criterion which measures the prediction risk of the predictive density based on the Bayesian marginal likelihood from a frequentist point of view. We derive the criteria for selecting variables in linear regression models by putting the prior on the regression...

In this article, we consider the problem of testing the equality of mean vectors of dimension ρ of several groups with a common unknown non-singular covariance matrix Σ, based on <em>N</em> independent observation vectors where <em>N</em> may be less than the dimension ρ. This problem, known in the literature...

The Akaike information criterion, AIC, and Mallows' Cp statistic have been proposed for selecting a smaller number of regressor variables in the multivariate regression models with fully unknown covariance matrix. All these criteria are, however, based on the implicit assumption that the sample...

The problem of classifying a new observation vector into one of the two known groups distributed as multivariate normal with common covariance matrix is consid- ered. In this paper, we handle the situation that the dimension, p, of the observation vectors is less than the total number, N, of...

　　 The problem of estimating the covariance matrix of normal and non-normal distributions is addressed when both the sample size and the dimension of covariance matrix tend to innity. In this paper, we consider a class of ridge-type estimators which are linear combinations of the...

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 this paper, we consider the problem of estimating the covaraince matrix and the generalized variance when the observations follow a nonsingular multivariate normal distribution with unknown mean. A new method is presented to obtain a truncated estimator that utilizes the information available...