Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Uniform asymptotic properties of a nonparametric regression estimator of conditional tails

Yuri Goegebeur, Armelle Guillou, and Gilles Stupfler

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Abstract

We consider a nonparametric regression estimator of conditional tails introduced by Goegebeur, Y., Guillou, A., Schorgen, G. (2013). Nonparametric regression estimation of conditional tails – the random covariate case. It is shown that this estimator is uniformly strongly consistent on compact sets and its rate of convergence is given.

Résumé

Nous considérons l’estimateur à noyau de l’indice des valeurs extrêmes conditionnel présenté dans Goegebeur, Y., Guillou, A., Schorgen, G. (2013). Nonparametric regression estimation of conditional tails – the random covariate case. Nous montrons la consistance uniforme presque sûre de cet estimateur sur les compacts et nous calculons sa vitesse de convergence presque sûre.

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist., Volume 51, Number 3 (2015), 1190-1213.

Dates
Received: 22 November 2013
Accepted: 27 April 2014
First available in Project Euclid: 1 July 2015

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1435759245

Digital Object Identifier
doi:10.1214/14-AIHP624

Mathematical Reviews number (MathSciNet)
MR3365978

Zentralblatt MATH identifier
1326.62089

Subjects
Primary: 62G05: Estimation 62G20: Asymptotic properties 62G32: Statistics of extreme values; tail inference

Keywords
Tail-index Kernel estimation Strong uniform consistency

Citation

Goegebeur, Yuri; Guillou, Armelle; Stupfler, Gilles. Uniform asymptotic properties of a nonparametric regression estimator of conditional tails. Ann. Inst. H. Poincaré Probab. Statist. 51 (2015), no. 3, 1190--1213. doi:10.1214/14-AIHP624. https://projecteuclid.org/euclid.aihp/1435759245


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