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Objective Bayesian Analysis of Skew‐ t Distributions
Author(s) -
BRANCO MARCIA D'ELIA,
GENTON MARC G.,
LISEO BRUNERO
Publication year - 2013
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/j.1467-9469.2011.00779.x
Subject(s) - mathematics , frequentist inference , skew , prior probability , estimator , bayesian probability , univariate , maximum a posteriori estimation , statistics , scale parameter , bayesian inference , maximum likelihood , multivariate statistics , computer science , telecommunications
. 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.