Quasi-χ~2 Distribution and the Independence of Wishart Distribution

In this paper, the authors generalize the definition of χ 2 distribution and introduce a quasi χ 2 distribution, and then prove several properties of it, find the necessary and sufficient conditions of independence about multivariate normal distributions, matrix normal distributions and two parts of the Wishart distribution.

An Extension of the Non-central Wishart Distribution with Integer Shape Vector

This research paper deals with an extension of the non-central Wishart introduced in 1944 by Anderson and Girshick,that is the non-central Riesz distribution when the scale parameter is derived from a discrete vector.It is related to the matrix of normal samples with monotonous missing data.We characterize this distribution by means of its Laplace transform and we give an algorithm for generating it.Then we investigate,based on the method of the moment,the estimation of the parameters of the proposed model.The performance of the proposed estimators is evaluated by a numerical study.

COOPERATIVE MIMO SPECTRUM SENSING BASED ON RANDOM MATRIX THEORY

Random Matrix Theory (RMT) is a valuable tool for describing the asymptotic behavior of multiple systems,especially for large matrices. In this paper,using asymptotic random matrix theory,a new cooperative Multiple-Input Multiple-Output (MIMO) scheme for spectrum sensing is proposed,which shows how asymptotic free property of random matrices and the property of Wishart distribution can be used to assist spectrum sensing for Cognitive Radios (CRs). Simulations over Rayleigh fading and AWGN channels demonstrate the proposed scheme has better detection performance compared with the energy detection techniques even in the case of a small sample of observations.

The Superiority of Bayes Estimators in a Multivariate Linear Model with Respect to Normal-Inverse Wishart Prior

In this paper, the multivariate linear model Y = XB＋e, e ～ Nm×k（0, ImΣ） is considered from the Bayes perspective. Under the normal-inverse Wishart prior for （BΣ）, the Bayes estimators are derived. The superiority of the Bayes estimators of B and Σ over the least squares estimators under the criteria of Bayes mean squared error （BMSE） and Bayes mean squared error matrix （BMSEM） is shown. In addition, the Pitman Closeness （PC） criterion is also included to investigate the superiority of the Bayes estimator of B.

Some Comments on Zonal Polynomials and Their Expected Values with respect to Elliptical.Distributions

In this paper, we give alternative proofs of some results in [15] （Li R.,1997） about the expected value of zonal polynomials.

ON SINGULAR MATRIX VARIATE BETA DISTRIBUTION

In this paper the density of the matrix variate beta distribution of rank lower than itsdimensionality is obtained with respect to a suitably defined differential form under the condi-tion that the difference between the identity and this matrix has full rank. As preliminaries,the Jacobian of a transformation related to decomposing a nonnegative-definite matrix into theproduct of a matrix of full column rank and its transpose and that of the transformation of anonnegative-definite matrix into its congruent matrix are established.

Modeling correlated samples via sparse matrix Gaussian graphical models

A new procedure of learning in Gaussian graphical models is proposed under the assumption that samples are possibly dependent.This assumption,which is pragmatically applied in various areas of multivariate analysis ranging from bioinformatics to finance,makes standard Gaussian graphical models(GGMs) unsuitable.We demonstrate that the advantage of modeling dependence among samples is that the true discovery rate and positive predictive value are improved substantially than if standard GGMs are applied and the dependence among samples is ignored.The new method,called matrix-variate Gaussian graphical models(MGGMs),involves simultaneously modeling variable and sample dependencies with the matrix-normal distribution.The computation is carried out using a Markov chain Monte Carlo(MCMC) sampling scheme for graphical model determination and parameter estimation.Simulation studies and two real-world examples in biology and finance further illustrate the benefits of the new models.