Bayesian variable selection and estimation in maximum entropy quantile regression

Quantile regression has gained increasing popularity as it provides richer information than the regular mean regression, and variable selection plays an important role in the quantile regression model building process, as it improves the prediction accuracy by choosing an appropriate subset of regression predictors. Unlike the traditional quantile regression, we consider the quantile as an unknown parameter and estimate it jointly with other regression coefficients. In particular, we adopt the Bayesian adaptive Lasso for the maximum entropy quantile regression. A flat prior is chosen for the quantile parameter due to the lack of information on it. The proposed method not only addresses the problem about which quantile would be the most probable one among all the candidates, but also reflects the inner relationship of the data through the estimated quantile. We develop an efficient Gibbs sampler algorithm and show that the performance of our proposed method is superior than the Bayesian adaptive Lasso and Bayesian Lasso through simulation studies and a real data analysis.