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A moving window approach for nonparametric estimation of the conditional tail index

Laurent Gardes 1 Stephane Girard 1
1 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology, LJK - Laboratoire Jean Kuntzmann, Inria Grenoble - Rhône-Alpes
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. A moving window approach for nonparametric estimation of the conditional tail index. Journal of Multivariate Analysis, Elsevier, 2008, 99 (10), pp.2368-2388. ⟨10.1016/j.jmva.2008.02.023⟩. ⟨inria-00124637v2⟩

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