Stepwise multiple quantile regression estimation using non-crossing constraints

Abstract

Quantile regression is an important statistical tool for statistical modeling. It has been widely used in various fields including econometrics, medicine, and bioinformatics. Despite its popularity in practice, individually estimated quantile regression functions often cross each other and consequently violate the basic properties of quantiles. In this paper we propose a new method for estimating multiple quantile regression functions without crossing. Both linear and kernel quantile regression models are considered. Several numerical examples are presented to illustrate competitive performance of the proposed method.