Extensions of Bayesian quantile regression models

Abstract

Since the seminal work of Koenker and Bassett (1978) quantile regression models have been used in several areas, with the interest in obtaining a more complete picture of the conditional distribution of the response variable as a function of covariates. Moyeed and Yu (2001) presented the first results for Bayesian quantile regression models considering the asymmetric Laplace distribution for the errors of the model. This project aims at the extension of the Bayesian quantile regression models for the case of excess of zeros in view of the Gibbs sampling proposed by Kozumi and Kobayashi (2011). There is also interest in generalizing the results to partially linear models. Furthermore, we will use the power priori approach of Ibrahim and Chen (2000) to extend the work of Alhamzawi and Yu (2012) for variable selection methods. This project also intends to provide a comprehensive study of sensitivity, through diagnostic techniques such as analysis of influence. The theoretical results will be implemented in software R and, if possible, will be made available in packages in the repository www.cran.r-project.org. Beyond that, simulation studies will be made to evaluate the methods proposed in this thesis, as well as databases will be used to compare obtained results with methods already proposed in the literature.