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

Quantile regression model is widely used in variable relationship research of general size data, due to strong robustness and more comprehensive description of the response variables' characteristics. With the increase of data size and data dimension, there have been some studies on high-dimensional quantile regression under the classical statistical framework, including higher-efficient frequency perspective, which is however at cost of randomness quantification, or lower-efficient Bayesian method based on MCMC sampling. To overcome these problems, we propose the high-dimensional quantile regression with 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. The simulation studies and real data analysis illustrate that the proposed VBSSLQR method is superior to or equivalent to other quantile and non-quantile regression methods (including Bayesian and non-Bayesian methods), and its efficiency is higher than any other method.