It is shown that Hill's estimator (1975) for the exponent of regular variation is asymptotically normal if the number $k_n$ of extreme order statistics used to construct it tends to infinity appropriately with the sample size $n.$ As our main result, we derive a general condition which can be used to determine the optimal $k_n$ explicitly, provided that some prior knowledge is available on the underlying distribution function with regularly varying upper tail. This condition is simplified under appropriate assumptions and then applied to several examples.
Publié le : 1985-06-14
Classification:
Regular variation,
parameter estimation,
order statistics,
limit theorems,
62G05,
62G30,
62F12
@article{1176349551,
author = {Haeusler, E. and Teugels, J. L.},
title = {On Asymptotic Normality of Hill's Estimator for the Exponent of Regular Variation},
journal = {Ann. Statist.},
volume = {13},
number = {1},
year = {1985},
pages = { 743-756},
language = {en},
url = {http://dml.mathdoc.fr/item/1176349551}
}
Haeusler, E.; Teugels, J. L. On Asymptotic Normality of Hill's Estimator for the Exponent of Regular Variation. Ann. Statist., Tome 13 (1985) no. 1, pp. 743-756. http://gdmltest.u-ga.fr/item/1176349551/