We use the fitted Pareto law to construct an accompanying approximation of the excess distribution function. A selection rule of the location of the excess distribution function is proposed based on a stagewise lack-of-fit testing procedure. Our main result is an oracle type inequality for the Kullback–Leibler loss.
Publié le : 2008-08-15
Classification:
Nonparametric adaptive estimation,
extreme values,
Hill estimator,
probabilities of rare events,
high quantiles,
62G32,
62G08,
62G05
@article{1216237294,
author = {Grama, Ion and Spokoiny, Vladimir},
title = {Statistics of extremes by oracle estimation},
journal = {Ann. Statist.},
volume = {36},
number = {1},
year = {2008},
pages = { 1619-1648},
language = {en},
url = {http://dml.mathdoc.fr/item/1216237294}
}
Grama, Ion; Spokoiny, Vladimir. Statistics of extremes by oracle estimation. Ann. Statist., Tome 36 (2008) no. 1, pp. 1619-1648. http://gdmltest.u-ga.fr/item/1216237294/