| Issue |
ESAIM: PS
Volume 18, 2014
|
|
|---|---|---|
| Page(s) | 642 - 666 | |
| DOI | https://doi.org/10.1051/ps/2013050 | |
| Published online | 15 October 2014 | |
Uniform strong consistency of a frontier estimator using kernel regression on high order moments
1
Team Mistis, INRIA Rhône-Alpes & LJK, Inovallée, 655, av.
de l’Europe, Montbonnot, 38334
Saint-Ismier cedex,
France
stephane.girard@inria.fr
2
Université de Strasbourg & CNRS, IRMA, UMR
7501, 7 rue René
Descartes, 67084
Strasbourg cedex,
France
3
Aix Marseille Université, CERGAM, EA 4225, 15-19 allée Claude Forbin,
13628
Aix-en-Provence cedex 1,
France
Received: 13 December 2012
Revised: 16 July 2013
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.
Mathematics Subject Classification: 62G05 / 62G20
Key words: Frontier estimation / kernel estimation / strong uniform consistency / Hall class
© EDP Sciences, SMAI, 2014
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