Bayesian analysis of generalized elliptical semi-parametric models. Issue 8 (10th June 2016)

• Record Type: Journal Article
• Authors: Rondon, Luz Marina; Bolfarine, Heleno
• Is Part Of: Journal of applied statistics. Volume 43:Issue 8(2016)
• Page Start: 1508
• Page End: 1524
• Publication Date: 2016-06-10
• Subjects: Bayesian analysis -- MCMC algorithm -- B-splines -- scale mixtures of normal distributions -- semi-parametric models -- R package; Statistics -- Periodicals; 519.5
• DOI: 10.1080/02664763.2015.1109070
• Languages: English
• ISSNs: 0266-4763

Abstract

Abstract : In this paper, we study the statistical inference based on the Bayesian approach for regression models with the assumption that independent additive errors follow normal, Student- t, slash, contaminated normal, Laplace or symmetric hyperbolic distribution, where both location and dispersion parameters of the response variable distribution include nonparametric additive components approximated by B -splines. This class of models provides a rich set of symmetric distributions for the model error. Some of these distributions have heavier or lighter tails than the normal as well as different levels of kurtosis. In order to draw samples of the posterior distribution of the interest parameters, we propose an efficient Markov Chain Monte Carlo (MCMC) algorithm, which combines Gibbs sampler and Metropolis–Hastings algorithms. The performance of the proposed MCMC algorithm is assessed through simulation experiments. We apply the proposed methodology to a real data set. The proposed methodology is implemented in the R package BayesGESM using the functiongesm() .