This paper consists of two parts. An easy proof is given for the weak consistency of Pickands' estimate for the main parameter of an extreme-value distribution. Moreover, further natural conditions are given for strong consistency and for asymptotic normality of the estimate. Next a large quantile of a distribution is estimated by a combination of extreme or intermediate order statistics. This leads to an asymptotic confidence interval.
Publié le : 1989-12-14
Classification:
Extreme-value theory,
order statistics,
strong consistency,
asymptotic normality,
62F12,
62G30
@article{1176347396,
author = {Dekkers, Arnold L. M. and Haan, Laurens De},
title = {On the Estimation of the Extreme-Value Index and Large Quantile Estimation},
journal = {Ann. Statist.},
volume = {17},
number = {1},
year = {1989},
pages = { 1795-1832},
language = {en},
url = {http://dml.mathdoc.fr/item/1176347396}
}
Dekkers, Arnold L. M.; Haan, Laurens De. On the Estimation of the Extreme-Value Index and Large Quantile Estimation. Ann. Statist., Tome 17 (1989) no. 1, pp. 1795-1832. http://gdmltest.u-ga.fr/item/1176347396/