High-Dimensional Variable Selection for Quantile Regression Based on Variational Bayesian Method

Abstract

The quantile regression model is widely used in variable relationship research of moderate sized data, due to its strong robustness and more comprehensive description of response variable characteristics. With the increase of data size and data dimensions, there have been some studies on high-dimensional quantile regression under the classical statistical framework, including a high-efficiency frequency perspective; however, this comes at the cost of randomness quantification, or the use of a lower efficiency Bayesian method based on MCMC sampling. To overcome these problems, we propose high-dimensional quantile regression with a spike-and-slab lasso penalty based on variational Bayesian (VBSSLQR), which can, not only improve the computational efficiency, but also measure the randomness via variational distributions. Simulation studies and real data analysis illustrated that the proposed VBSSLQR method was superior or equivalent to other quantile and nonquantile regression methods (including Bayesian and non-Bayesian methods), and its efficiency was higher than any other method.