A note on extreme values and kernel estimators of sample boundaries
Abstract
In a previous paper, we studied a kernel estimate of the upper edge of a two-dimensional bounded set, based upon the extreme values of a Poisson point process. The initial paper "Geffroy J. (1964) Sur un probl\`eme d'estimation g\'eom\'etrique.Publications de l'Institut de Statistique de l'Universit\'e de Paris, XIII, 191-200" on the subject treats the frontier as the boundary of the support set for a density and the points as a random sample. We claimed in"Girard, S. and Jacob, P. (2004) Extreme values and kernel estimates of point processes boundaries.ESAIM: Probability and Statistics, 8, 150-168" that we are able to deduce the random sample case fr om the point process case. The present note gives some essential indications to this end, including a method which can be of general interest.
Cite
@article{arxiv.1208.6378,
title = {A note on extreme values and kernel estimators of sample boundaries},
author = {Stéphane Girard and Pierre Jacob},
journal= {arXiv preprint arXiv:1208.6378},
year = {2012}
}