MM Algorithms for Statistical Estimation in Quantile Regression

TL;DR

This paper develops and tests MM algorithms for linear quantile regression, demonstrating their simplicity, efficiency, and superiority over some existing methods through simulations and real data applications.

Contribution

It introduces a new class of MM algorithms for quantile regression that are easy to implement and outperform some existing methods in nonregularized settings.

Findings

MM algorithms are simple to code and effective.

Simulation studies show superior performance of MM algorithms.

Real data applications confirm practical usefulness.

Abstract

Quantile regression \parencite{Koenker1978} is a robust and practically useful way to efficiently model quantile varying correlation and predict varied response quantiles of interest. This article constructs and tests MM algorithms, which are simple to code and have been suggested superior to some other prominent quantile regression methods in nonregularized problems \parencite{Pietrosanu2017}, in an array of linear quantile regression settings. Simulation studies comparing MM to existing tested methods and applications to various real data sets have corroborated our algorithms' effectiveness.