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

Authors:
Laurent Gardes;Stéphane Girard
Affiliations:
INRIA Rhône-Alpes, team Mistis, 655, avenue de l'Europe, Montbonnot, 38334 Saint-Ismier Cedex, France;INRIA Rhône-Alpes, team Mistis, 655, avenue de l'Europe, Montbonnot, 38334 Saint-Ismier Cedex, France
Venue:
Journal of Multivariate Analysis
Year:
2008

Citing 4
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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.