Bayesian bridge and reciprocal bridge composite quantile regression

Abstract

Bayesian regularized composite quantile regression approaches with bridge and reciprocal bridge penalties are adopted to conduct variable selection in composite quantile regression. Two MCMC algorithms were developed for posterior inference using the normal-exponential mixture representation of the asymmetric Laplace distribution. Gamma prior is placed on the regularization parameter. The parameters of the Gamma prior are treated as unknowns and estimate them along with the other parameters. The performance of the proposed composite quantile regression methods over the existing methods is then illustrated via simulated studies and a real data set.