Bayesian joint inference for multivariate quantile regression model with L$$_{1/2}$$ penalty

Abstract

This paper considers a Bayesian approach for joint estimation of the marginal conditional quantiles from several dependent variables under a linear regression framework. This approach incorporates the dependence among different dependent variables in the regression model which studies how the relationship between dependent variables and a set of explanatory variables can vary across different quantiles of the marginal conditional distribution of the dependent variables. A Bayesian regularization approach with L 1/2 penalty is adopted to conduct high-dimensional variable selection. Some simulation studies are conducted to evaluate the performance of our proposed method. We illustrate the proposed estimation approach using a real data set on energy efficiency with two responses.