Statistics and Its Interface

Volume 2 (2009)

Number 3

Stepwise multiple quantile regression estimation using non-crossing constraints

Pages: 299 – 310



Yufeng Liu (Department of Statistics and Operations Research, Carolina Center for Genome Sciences, University of North Carolina, Chapel Hill, N.C., U.S.A.)

Yichao Wu (Department of Statistics, North Carolina State University, Raleigh, N.C., U.S.A.)


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.


Constraints, non-crossing, quantile regression, RKHS, variable selection

2010 Mathematics Subject Classification

Primary 62G08, 62J05. Secondary 62H12.

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