Computation in quantile and composite quantile regression models with or without regularization

Abstract

Quantile, composite quantile regression with or without regularization have been widely studied and applied in the high-dimensional model estimation and variable selections. Although the theoretical aspect has been well established, the lack of efficient computation methods and publicly available programs or packages hinder the research in this area. Koenker has established and implemented the interior point(IP) method in quantreg for quantile regression with or without regularization. However, it still lacks the ability to handle the composite quantile regression with or without regularization. The same incapability also existed in Coordinate Descent (CD) algorithm that has been implemented in CDLasso. The lack of handful programs for composite quantile regression with or without regularization motivates our research here. In this work, we implement three different algorithms including Majorize and Minimize(MM), Coordinate Descent(CD) and Alternation Direction Method of Multiplier(ADMM) for quantile and composite quantile regression with or without regularization. We conduct the simulation that compares the performance of four algorithms in time efficiency and estimation accuracy. The simulation study shows our program is time efficient when dealing with high dimensional problems. Based on the good performance of our program, we publish the R package cqrReg, which give the user more flexibility and capability when directing various data analyses. In order to optimize the time efficiency, the package cqrReg is coded in C++ and linked back to R by an user-friendly interface.