Estimation of the tail-index in a conditional location-scale family of heavy-tailed distributions

Aboubacrène Ag Ahmad 1 , El Hadji Deme 1 , Aliou Diop 1 , and Stéphane Girard 2
  • 1 Université Gaston Berger, LERSTAD, UFR SAT, Saint-Louis
  • 2 Univ. Grenoble Alpes, , 38000, Grenoble, France

Abstract

We introduce a location-scale model for conditional heavy-tailed distributions when the covariate is deterministic. First, nonparametric estimators of the location and scale functions are introduced. Second, an estimator of the conditional extreme-value index is derived. The asymptotic properties of the estimators are established under mild assumptions and their finite sample properties are illustrated both on simulated and real data.

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