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.
A. Christmann and I. Steinwart, Consistency of Kernel Based Quantile Regression. Applied Stochastic Models in Business and Industry, Vol. 24, pp. 171-183, 2008. Los Alamos National Laboratory Technical Report LA-UR-06-7110, 2006. [ Abstract | PDF (227 KB) ]
