2024/06/05 by João Victor B. de Freitas, de Freitas, João Victor B., Caio Azevedo +1
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Statistical Distribution Estimation and Applications #Statistical Methods and Bayesian Inference
paper · pdf · doi:10.48550/arxiv.2406.03432
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.