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Uniform strong consistency of a frontier estimator using kernel regression on high order moments

Published online by Cambridge University Press:  15 October 2014

Stéphane Girard ,
Armelle Guillou  and
Gilles Stupfler
Stéphane Girard
Affiliation:
Team Mistis, INRIA Rhône-Alpes & LJK, Inovallée, 655, av. de l’Europe, Montbonnot, 38334 Saint-Ismier cedex, France. stephane.girard@inria.fr
Armelle Guillou
Affiliation:
Université de Strasbourg & CNRS, IRMA, UMR 7501, 7 rue René Descartes, 67084 Strasbourg cedex, France
Gilles Stupfler
Affiliation:
Aix Marseille Université, CERGAM, EA 4225, 15-19 allée Claude Forbin, 13628 Aix-en-Provence cedex 1, France
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Abstract

We consider the high order moments estimator of the frontier of a random pair, introduced by [S. Girard, A. Guillou and G. Stupfler, J. Multivariate Anal. 116 (2013) 172–189]. In the present paper, we show that this estimator is strongly uniformly consistent on compact sets and its rate of convergence is given when the conditional cumulative distribution function belongs to the Hall class of distribution functions.

Keywords

Frontier estimationkernel estimationstrong uniform consistencyHall class
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 18 , 2014 , pp. 642 - 666
Copyright
© EDP Sciences, SMAI, 2014

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