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Activity Number:
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398
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Type:
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Invited
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Date/Time:
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Wednesday, August 1, 2007 : 10:30 AM to 12:20 PM
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Sponsor:
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IMS
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| Abstract - #307939 |
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Title:
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Learnability and Robustness of Nonparametric Quantile Regression
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Author(s):
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Andreas Christmann*+ and Ingo Steinwart
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Companies:
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Free University of Brussels VUB and Los Alamos National Laboratory
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Address:
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Department of Mathematics, Brussels, 1050, Belgium
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Keywords:
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quantile regression ; empirical risk minimization ; consistency ; kernel ; non-parametric
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Abstract:
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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 proposed by Takeuchi et al. (2006) shares with support vector machines the property of consistency to the smallest possible risk (i.e., to the Bayes risk). Further we use this consistency to prove that the non-parametric generalization approximates the conditional quantile function which gives the mathematical justification that kernel based quantile regression is able to learn. Some results concerning robustness properties of such regression estimators are also given.
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