We introduce a new estimate of the exponent of a distribution whose tail varies regularly at infinity. This estimate is expressed as the convolution of a kernel with the logarithm of the quantile function, and includes as particular cases the estimates introduced by Hill and by De Haan. Under very weak conditions, we prove asymptotic normality, consistency and discuss the optimal choices of the kernel and of the bandwidth parameter.
Publié le : 1985-09-14
Classification:
Pareto distribution,
order statistics,
nonparametric estimation,
empirical processes,
quantile process,
regularly varying functions,
62G05,
62G30
@article{1176349656,
author = {Csorgo, Sandor and Deheuvels, Paul and Mason, David},
title = {Kernel Estimates of the Tail Index of a Distribution},
journal = {Ann. Statist.},
volume = {13},
number = {1},
year = {1985},
pages = { 1050-1077},
language = {en},
url = {http://dml.mathdoc.fr/item/1176349656}
}
Csorgo, Sandor; Deheuvels, Paul; Mason, David. Kernel Estimates of the Tail Index of a Distribution. Ann. Statist., Tome 13 (1985) no. 1, pp. 1050-1077. http://gdmltest.u-ga.fr/item/1176349656/