Consistency of kernel-based quantile regression

Authors:
Andreas Christmann;Ingo Steinwart
Affiliations:
Department of Mathematics, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussel, Belgium;CCS-3, Mail Stop B256, Los Alamos National Laboratory, Los Alamos, NM 87545, U.S.A.
Venue:
Applied Stochastic Models in Business and Industry
Year:
2008

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Abstract

Quantile regression is used in many areas of applied research and business. Examples are actuarial, financial or biometrical applications. We show that a non-parametric generalization of quantile regression based on kernels shares with support vector machines the property of consistency to the Bayes risk. We further use this consistency to prove that the non-parametric generalization approximates the conditional quantile function which gives the mathematical justification for kernel-based quantile regression. Copyright © 2008 John Wiley & Sons, Ltd.