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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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References:
 [1] Adcock, Asset Pricing and Portfolio Selection Based on the Multivariate Skew-Student Distribution (2002) · Zbl 1233.91112 [2] Aigner, Formulation and estimation of stochastic frontier production function model, Journal of Econometrics 12 pp 21– (1977) · Zbl 0366.90026 [3] Arnold, Hidden truncation models, Sankhyǎ, Series A 62 pp 23– (2000) [4] Arnold, Skewed multivariate models related to hidden truncation and/or selective reporting (with discussion), Test 11 pp 7– (2002) · Zbl 1033.62013 [5] Azzalini, Statistical applications of the multivariate skew normal distribution, Journal of the Royal Statistical Society Series B 61 pp 579– (1999) · Zbl 0924.62050 [6] Azzalini, The multivariate skew-normal distribution, Biometrika 8 pp 715– (1996) · Zbl 0885.62062 [7] Bernardo, Bayesian Theory. (1994) [8] Branco, Bayesian analysis of calibration problem under elliptical distributions, Journal of Statistical Planning and Inference 90 pp 69– (2000) · Zbl 1066.62040 [9] Branco, A general class of multivariate skew elliptical distributions, Journal of Multivariate Analysis 79 pp 99– (2001) · Zbl 0992.62047 [10] Chen, A new skewed link model for dichotomous quantal response data, Journal of the American Statistical Association 94 pp 1172– (1999) · Zbl 1072.62655 [11] Chib, Bayes prediction in regressions with elliptical errors, Journal of Econometrics 38 pp 349– (1988) · Zbl 0677.62030 [12] DiCiccio, Computing Bayes factors by combining simulation and asymptotic approximations, Journal of the American Statistical Association 92 pp 903– (1997) · Zbl 1050.62520 [13] Fang, Symmetric Multivariate and Related Distributions. (1990) [14] Fernandez, On Bayesian modeling of fat tails and skewness, Journal of the American Statistical Association 93 pp 359– (1998) [15] Gelfand, Bayesian model choice-Asymptotics and exact calculations, Journal of the Royal Statistical Society Series B 56 pp 501– (1994) · Zbl 0800.62170 [16] Geweke, Bayesian treatment of the independent Student-i linear model, Journal of Applied Econometrics 8 pp 519– (1993) [17] Huang, Foundations for Financial Economics. (1988) · Zbl 0677.90001 [18] Jones, Probability and Statistical Models with Applications pp 269– (2001) [19] Kelker, Distribution theory of spherical distributions and a location-scale parameter generalization, Sankhyà 32 pp 419– (1970) · Zbl 0223.60008 [20] Mardia, Measures of multivariate skewness and kurtosis with applications, Biometrika 57 pp 519– (1970) · Zbl 0214.46302 [21] Osiewalski, Robust Bayesian inference in elliptical regression models, Journal of Econometrics 57 pp 345– (1993) · Zbl 0776.62029 [22] Spiegelhalter, Bayesian measures of model complexity and fit (with discussion), Journal of the Royal Statistical Society Series B 64 pp 583– (2002) · Zbl 1067.62010 [23] Spiegelhalter, Bayesian Statistics 5: Proceedings of the 5th Valencia International Meeting Held in Alicante, June 5-9, 1994 pp 407– (1996) [24] Whittaker, A Course of Modern Analysis: An Introduction to the General Theory of Infinite Processes and of Analytic Functions. (1927) · JFM 53.0180.04 [25] Zellner, Bayesian and non-Bayesian analysis of the regression model with multivariate Student-t error term, Journal of the American Statistical Association 11 pp 400– (1976) · Zbl 0348.62026
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