Empirical Bayes Estimation in Regression Models with Generalized Skew-Slash Errors

Autor:	Majid Jafari Khaledi, Hamid Zareifard
Rok vydání:	2013
Předmět:	Statistics and Probability Bayes estimator Proper linear model Statistics Prior probability Maximum a posteriori estimation Statistics::Methodology Bayesian hierarchical modeling Bayes factor Bayesian linear regression Statistics::Computation Mathematics Empirical Bayes method
Zdroj:	Communications in Statistics - Theory and Methods. 42:1105-1123
ISSN:	1532-415X 0361-0926
DOI:	10.1080/03610926.2011.593282
Popis:	In this article, utilizing a scale mixture of skew-normal distribution in which mixing random variable is assumed to follow a mixture model with varying weights for each observation, we introduce a generalization of skew-normal linear regression model with the aim to provide resistant results. This model, which also includes the skew-slash distribution in a particular case, allows us to accommodate and detect outlying observations under the skew-normal linear regression model. Inferences about the model are carried out through the empirical Bayes approach. The conditions for propriety of the posterior and for existence of posterior moments are given under the standard noninformative priors for regression and scale parameters as well as proper prior for skewness parameter. Then, for Bayesian inference, a Markov chain Monte Carlo method is described. Since posterior results depend on the prior hyperparameters, we estimate them adopting the empirical Bayes method as well as using a Monte Carlo EM algorithm. ...
Databáze:	OpenAIRE
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