The cqrReg package for R is the first to introduce a family of robust,high-dimensional regression models for quantile and composite quantileregression, both with and without an adaptive lasso penalty for variableselection. In this paper, we reformulate these quantile regression problems andpresent the estimators we implement in cqrReg using alternating directionmethod of multipliers (ADMM), majorize-minimization (MM), and coordinatedescent (CD) algorithms. Our new approaches address the lack ofpublicly-available methods for (composite) quantile regression, both with andwithout regularization. We demonstrate the need for a variety of algorithms inlater simulation studies. For comparison, we also introduce the widely-usedinterior point (IP) formulation and test our methods against the advanced IPalgorithms in the existing quantreg package. Our simulation studies show thateach of our methods, particularly MM and CD, excel in different settings suchas with large or high-dimensional data sets, respectively, and outperform themethods currently implemented in quantreg. ADMM offers particular promise forfuture developments in its amenability to parallelization.
展开▼
