Objective Bayesian Analysis of Skew-t Distributions

Autor(es)

Branco, Marcia D'Elia ^[1] ; Genton, Marc G. ^[2] ; Liseo, Brunero ^[3]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Dept Estat, BR-05508 Sao Paulo - Brazil

^[2] Texas A&M Univ, Dept Stat, College Stn, TX 77843 - USA

^[3] Univ Roma La Sapienza, MEMOTEF, Rome - Italy

• Tipo de documento: Artigo Científico
• Fonte: SCANDINAVIAN JOURNAL OF STATISTICS; v. 40, n. 1, p. 63-85, MAR 2013.
• Citações Web of Science: 10

Resumo

. We study the Jeffreys prior and its properties for the shape parameter of univariate skew-t distributions with linear and nonlinear Student's t skewing functions. In both cases, we show that the resulting priors for the shape parameter are symmetric around zero and proper. Moreover, we propose a Student's t approximation of the Jeffreys prior that makes an objective Bayesian analysis easy to perform. We carry out a Monte Carlo simulation study that demonstrates an overall better behaviour of the maximum a posteriori estimator compared with the maximum likelihood estimator. We also compare the frequentist coverage of the credible intervals based on the Jeffreys prior and its approximation and show that they are similar. We further discuss location-scale models under scale mixtures of skew-normal distributions and show some conditions for the existence of the posterior distribution and its moments. Finally, we present three numerical examples to illustrate the implications of our results on inference for skew-t distributions. (AU)

• Processo FAPESP: 04/15304-6 - Modelos de regressão e aplicações
• Beneficiário: Heleno Bolfarine
• Modalidade de apoio: Auxílio à Pesquisa - Temático