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A new class of multivariate skew distributions with applications to Bayesian regression models. (English) Zbl 1039.62047
Can. J. Stat. 31, No. 2, 129-150 (2003); erratum ibid. 301-302 (2009).
Summary: The authors develop a new class of distributions by introducing skewness in multivariate elliptically symmetric distributions. The class, which is obtained by using transformation and conditioning, contains many standard families including the multivariate skew-normal and \(t\) distributions. The authors obtain analytical forms of the densities and study distributional properties. They give practical applications in Bayesian regression models and results on the existence of the posterior distributions and moments under improper priors for the regression coefficients. They illustrate their methods using practical examples.

MSC:
62H05 Characterization and structure theory for multivariate probability distributions; copulas
62F15 Bayesian inference
62J05 Linear regression; mixed models
62H12 Estimation in multivariate analysis
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