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Graphical models for skew‐normal variates
Author(s) -
CAPITANIO A.,
AZZALINI A.,
STANGHELLINI E.
Publication year - 2003
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.00322
Subject(s) - mathematics , graphical model , univariate , conditional independence , factorization , exponential family , independence (probability theory) , multivariate normal distribution , multivariate statistics , skew , marginal distribution , graph , extension (predicate logic) , conditional expectation , context (archaeology) , statistics , random variable , discrete mathematics , algorithm , computer science , telecommunications , paleontology , biology , programming language
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 Azzalini & Dalla Valle (1996) and Azzalini & Capitanio (1999) 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.