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Consistency of kernel‐based quantile regression
Author(s) -
Christmann Andreas,
Steinwart Ingo
Publication year - 2008
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.700
Subject(s) - quantile regression , consistency (knowledge bases) , quantile , generalization , econometrics , kernel regression , mathematics , kernel (algebra) , quantile function , semiparametric regression , parametric statistics , computer science , statistics , nonparametric statistics , probability distribution , discrete mathematics , mathematical analysis , moment generating function
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.