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Bayesian inference for scale mixtures of skew-normal linear models under the centered parameterization
- Publication Year :
- 2024
-
Abstract
- In many situations we are interested in modeling real data where the response distribution, even conditionally on the covariates, presents asymmetry and/or heavy/light tails. In these situations, it is more suitable to consider models based on the skewed and/or heavy/light tailed distributions, such as the class of scale mixtures of skew-normal distributions. The classical parameterization of this distributions may not be good due to the some inferential issues when the skewness parameter is in a neighborhood of 0, then, the centered parameterization becomes more appropriate. In this paper, we developed a class of scale mixtures of skew-normal distributions under the centered parameterization, also a linear regression model based on them was proposed. We explore a hierarchical representation and set up a MCMC scheme for parameter estimation. Furthermore, we developed residuals and influence analysis tools. A Monte Carlo experiment is conducted to evaluate the performance of the MCMC algorithm and the behavior of the residual distribution. The methodology is illustrated with the analysis of a real data set.
- Subjects :
- Statistics - Methodology
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2406.03432
- Document Type :
- Working Paper