Sampling Lasso quantile regression for large-scale data

With the quantile regression methods successfully applied in various applications, we often need to tackle with the big dataset with thousands of variables and millions of observations. In this article, we focus on the variable selection aspect of penalized quantile regression, and propose a new method Sampling Lasso Quantile Regression (SLQR), which allows selecting a small amount but informative data for fitting quantile regression models. Different from the ordinary regularization methods, this SLQR method performs a sampling technique to reduce the number of observations before applying Lasso. Through numerical simulation studies and real application in Greenhouse Gas Observing Network, we illustrate the efficacy of the SLQR method. The numerical results show that the SLQR method is able to achieve a high-precision quantile regression on large-scale data for both prediction and interpretation.