Bayesian Analysis of Composite Quantile Regression

This paper introduces a Bayesian approach for composite quantile regression employing the skewed Laplace distribution for the error distribution. We use a two-level hierarchical Bayesian model for coefficient estimation and future selection which assumes a prior distribution that favors sparseness. An efficient Gibbs sampling algorithm is developed to update the unknown quantities from the posteriors. The proposed approach is illustrated via simulation studies and two real datasets. Results indicate that the proposed approach performs quite good in comparison to the other approaches.