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Nonparametric estimation of the conditional tail index

Laurent Gardes 1 Stephane Girard 1
1 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology
Abstract : We present a nonparametric family of estimators for the tail index of a Pareto-type distribution when covariate information is available. Our estimators are based on a weighted sum of the log-spacings between some selected observations. This selection is achieved through a moving window approach on the covariate domain and a random threshold on the variable of interest. Asymptotic normality is proved under mild regularity conditions and illustrated for some weight functions. Finite sample performances are presented on a real data study.
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Laurent Gardes, Stephane Girard. Nonparametric estimation of the conditional tail index. Statistical Extremes and Environmental Risk Workshop, Feb 2007, Lisbonne, Portugal. pp.47-50. ⟨hal-00987250⟩

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