Name: Simone Bega Harnik
Institution: IME, USP, Brazil
E-mail: siharnik@gmail.com
Co-authors: Márcia D’Elia Branco
Abstract:
Skew-t regression models have been considered a robust alternative when compared to models with normally distributed errors. As they have flexibility to deal with data with asymmetry and heavier tails than the normal ones, skew-t models are usually applied in various areas, such as biology, economy, social sciences, among others. However, because of the asymmetry of this model, outlier position has an important role in the study of robustness and more detailed investigation should be conducted. In this work we assess robustness to outliers in skew-t, skew-normal and normal models under the Bayesian perspective by making use of divergence measures – Kullback-Leibler divergence and L1-norm. An advantage of this method is to examine the whole posterior distribution and not only point estimates. Posterior divergence measures computation is based on Peng and Dey approach, by Monte Carlo estimation from samples of the parameters. We develop a simulation study in Stan, a platform for high-performance statistical computation in R, varying the proportion of contaminants, position of outliers (left, right or both tails) and skewness of error distributions. Summary measures of the posterior distribution are also provided. The final aim is to show whether skew-t models should be recommended because of its superior resistance to outliers.