Wishart distributions for decomposable covariance graph models

Details Wishart distributions for decomposable covariance graph models Wishart distributions for decomposable covariance graph models

2011-03-09

arxiv.org/abs/1103.1768v1

Annals of Statistics 2011, Vol. 39, No. 1, 514-555

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/10-AOS841 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

10.1214/10-AOS841

Gaussian covariance graph models encode marginal independence among the components of a multivariate random vector by means of a graph $G$. These models are distinctly different from the traditional concentration graph models (often also referred to as Gaussian graphical models or covariance selection models) since the zeros in the parameter are now reflected in the covariance matrix $\Sigma$, as compared to the concentration matrix $\Omega =\Sigma^{-1}$. The parameter space of interest for covariance graph models is the cone $P_G$ of positive definite matrices with fixed zeros corresponding to the missing edges of $G$. As in Letac and Massam [Ann. Statist. 35 (2007) 1278--1323], we consider the case where $G$ is decomposable. In this paper, we construct on the cone $P_G$ a family of Wishart distributions which serve a similar purpose in the covariance graph setting as those constructed by Letac and Massam [Ann. Statist. 35 (2007) 1278--1323] and Dawid and Lauritzen [Ann. Statist. 21 (1993) 1272--1317] do in the concentration graph setting. We proceed to undertake a rigorous study of these "covariance" Wishart distributions and derive several deep and useful properties of this class.

Affiliated with

Also associated with

No associations

Rating

Wishart distributions for decomposable covariance graph models does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Wishart distributions for decomposable covariance graph models, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Wishart distributions for decomposable covariance graph models will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-644332