Bayesian LASSO-Regularized Weighted Composite Quantile Regression

Regression models are traditionally estimated using the least square estimation (LSE) method which may result in non-robust parameter estimates when data includes non-normal feature or outliers. Compared to LSE approach, composite quantile regression (CQR) can provide more robust estimation results even suffering non-normal errors or outliers. Based on a composite asymmetric Laplace distribution (CALD), the weighted composite quantile regression (WCQR) can be treated in the Bayesian framework. Regularization methods have been verified to be very effective for high-dimensional sparse regression models in that it can simultaneously conduct variable selection and parameters estimation. In this paper, we combine Bayesian LASSO regularization methods with WCQR to fit linear regression models. Bayesian LASSO-regularized hierarchical models of WCQR are constructed and the conditional posterior distributions of all unknown parameters are derived to conduct statistical inference. Finally, the developed methods are illustrated by Monte Carlo simulations and a real data analysis.