Non-crossing convex quantile regression

TL;DR

This paper introduces a penalized convex quantile regression method that prevents quantile crossing and preserves the intrinsic quantile property, improving upon existing constrained approaches.

Contribution

It proposes a novel penalized approach for convex quantile regression that avoids quantile crossing while maintaining the quantile property, addressing limitations of previous methods.

Findings

Penalized convex quantile regression effectively prevents crossing.

The method better preserves the intrinsic quantile property.

Monte Carlo simulations show improved performance over existing methods.

Abstract

Quantile crossing is a common phenomenon in shape constrained nonparametric quantile regression. A recent study by Wang et al. (2014) has proposed to address this problem by imposing non-crossing constraints to convex quantile regression. However, the non-crossing constraints may violate an intrinsic quantile property. This paper proposes a penalized convex quantile regression approach that can circumvent quantile crossing while better maintaining the quantile property. A Monte Carlo study demonstrates the superiority of the proposed penalized approach in addressing the quantile crossing problem.