Applications of extreme value theory to problems of statistical inference typically involve estimating tail probabilities well beyond the range of the data, without the benefit of a concise mathematical model for the sampling distribution. The available model is generally only an asymptotic one. That is, an approximation to probabilities of extreme deviation is supposed, which is assumed to become increasingly accurate as one moves further from the
range of the data, but whose concise accuracy is unknown. Quantification of the level of accuracy is essential for optimal estimation of tail probabilities. In the present paper we suggest a practical device, based on a nonstandard
application of the bootstrap, for determining empirically the accuracy of the approximation and thereby constructing appropriate estimators.
Publié le : 1997-06-14
Classification:
Bootstrap,
extreme value,
Hill's estimator,
order statistic,
Pareto approximation,
regular variation,
smoothing,
60G70,
62G05,
62G09
@article{1069362750,
author = {Hall, Peter and Weissman, Ishay},
title = {On the estimation of extreme tail probabilities},
journal = {Ann. Statist.},
volume = {25},
number = {6},
year = {1997},
pages = { 1311-1326},
language = {en},
url = {http://dml.mathdoc.fr/item/1069362750}
}
Hall, Peter; Weissman, Ishay. On the estimation of extreme tail probabilities. Ann. Statist., Tome 25 (1997) no. 6, pp. 1311-1326. http://gdmltest.u-ga.fr/item/1069362750/