Graphical models for skew‐normal variates
Antonella Capitanio
Dipartimento di Scienze Statistiche, Università di Bologna, via delle Belle Arti 41,I‐40126 Bologna, Italy. E‐mail: capitani@stat.unibo.it
Abstract
This paper explores the usefulness of the multivariate skew‐normal distribution in the context of graphical models. A slight extension of the family recently discussed by 3) and 3) is described, the main motivation being the additional property of closure under conditioning. After considerations of the main probabilistic features, the focus of the paper is on the construction of conditional independence graphs for skew‐normal variables. Necessary and sufficient conditions for conditional independence are stated, and the admissible structures of a graph under restriction on univariate marginal distribution are studied. Finally, parameter estimation is considered. It is shown how the factorization of the likelihood function according to a graph can be rearranged in order to obtain a parameter based factorization.
Citing Literature
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