<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...

　　 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...

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 paper addresses the problem of selecting variables in the two-stage sampling models characterized as a linear mixed model. We obtain the Empirical Bayes Information Criterion (EBIC) using a prior distribution on regression coefficients with an unknown hyper-parameter. It is shown that EBIC...

In this paper, we consider the problem of selecting the variables of the fixed effects in the linear mixed models where the random effects are present and the observation vectors have been obtained from many clusters. As the variable selection procedure, we here use the Akaike Information...

The Akaike Information Criterion (AIC) is developed for selecting the variables of a nested error regression model where an unobservable random effect is present. Using the idea of decomposing the marginal distribution into two parts of 'within' and 'between' analysis of variance, we derive the...

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...

In this paper, we consider the problem of selecting variables from the fixed effects as well as from the random effects when observations from several clusters are available to provide consistent estimators of some unknown parameters. We obtain Bayesian Information Criterion (BIC) using the...