Given a general multivariate linear model of full or less than full rank, we find the distributions of internally and externally studentised residuals, assuming normal and elliptical distributions.

Univariate dispersive ordering has been extensively characterized by many authors over the last two decades. However, the multivariate version lacks extensive analysis. In this paper, sufficient and necessary conditions are given to preserve the strong multivariate dispersion order through...

For a sequence of independent and identically distributed random vectors , i=1,2,...,n, we consider the conditional ordering of these random vectors with respect to the magnitudes of , where N is a p-variate continuous function defined on the support set of X1 and satisfying certain regularity...

Two conditions are shown under which elliptical distributions are scale mixtures of normal distributions with respect to probability distributions. The issue of finding the mixing distribution function is also considered. As a unified theoretical framework, it is also shown that any scale...

We consider a panel data semiparametric partially linear regression model with an unknown vector [beta] of regression coefficients, an unknown nonparametric function g(·) for nonlinear component, and unobservable serially correlated errors. The correlated errors are modeled by a vector...

For the test of sphericity, Ledoit and Wolf [Ann. Statist. 30 (2002) 1081-1102] proposed a statistic which is robust against high dimensionality. In this paper, we consider a natural generalization of their statistic for the test that the smallest eigenvalues of a covariance matrix are equal....

In this paper we develop an econometric method for consistent variable selection in the context of a linear factor model with observable factors for panels of large dimensions. The subset of factors that best fit the data is sequentially determined. Firstly, a partial R2 rule is used to show the...

This paper considers image classification based on a Markov random field (MRF), where the random field proposed here adopts Jeffreys divergence between category-specific probability densities. The classification method based on the proposed MRF is shown to be an extension of Switzer's soothing...

In this article, the problem of classifying a new observation vector into one of the two known groups [Pi]i,i=1,2, distributed as multivariate normal with common covariance matrix is considered. The total number of observation vectors from the two groups is, however, less than the dimension of...

The common principal components (CPC) model for several groups of multivariate observations assumes equal principal axes but possibly different variances along these axes among the groups. Under a CPCs model, generalized projection-pursuit estimators are defined by using score functions on the...