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.
Mots-clés : frontier estimation, kernel estimation, strong uniform consistency, Hall class
@article{PS_2014__18__642_0,
author = {Girard, St\'ephane and Guillou, Armelle and Stupfler, Gilles},
title = {Uniform strong consistency of a frontier estimator using kernel regression on high order moments},
journal = {ESAIM: Probability and Statistics},
pages = {642--666},
publisher = {EDP-Sciences},
volume = {18},
year = {2014},
doi = {10.1051/ps/2013050},
mrnumber = {3334007},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ps/2013050/}
}
TY - JOUR AU - Girard, Stéphane AU - Guillou, Armelle AU - Stupfler, Gilles TI - Uniform strong consistency of a frontier estimator using kernel regression on high order moments JO - ESAIM: Probability and Statistics PY - 2014 SP - 642 EP - 666 VL - 18 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ps/2013050/ DO - 10.1051/ps/2013050 LA - en ID - PS_2014__18__642_0 ER -
%0 Journal Article %A Girard, Stéphane %A Guillou, Armelle %A Stupfler, Gilles %T Uniform strong consistency of a frontier estimator using kernel regression on high order moments %J ESAIM: Probability and Statistics %D 2014 %P 642-666 %V 18 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ps/2013050/ %R 10.1051/ps/2013050 %G en %F PS_2014__18__642_0
Girard, Stéphane; Guillou, Armelle; Stupfler, Gilles. Uniform strong consistency of a frontier estimator using kernel regression on high order moments. ESAIM: Probability and Statistics, Tome 18 (2014), pp. 642-666. doi : 10.1051/ps/2013050. http://archive.numdam.org/articles/10.1051/ps/2013050/
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