Nonparametric regression estimation of conditional tails: the random covariate case |
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Authors: | Yuri Goegebeur Armelle Guillou Antoine Schorgen |
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Institution: | 1. Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, 5230 Odense M, Denmarkyuri.goegebeur@imada.sdu.dk;3. Institut Recherche Mathématique Avancée, UMR 7501, Université de Strasbourg et CNRS, 7 rue René Descartes, 67084 Strasbourg cedex, France |
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Abstract: | We present families of nonparametric estimators for the conditional tail index of a Pareto-type distribution in the presence of random covariates. These families are constructed from locally weighted sums of power transformations of excesses over a high threshold. The asymptotic properties of the proposed estimators are derived under some assumptions on the conditional response distribution, the weight function and the density function of the covariates. We also introduce bias-corrected versions of the estimators for the conditional tail index, and propose in this context a consistent estimator for the second-order tail parameter. The finite sample performance of some specific examples from our classes of estimators is illustrated with a small simulation experiment. |
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Keywords: | tail index Pareto-type distribution regression kernel statistic bias-correction |
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