A Berry-Esseen bound of order $n^{-\frac{1}{2}}$ is established for linear combinations of order statistics. The theorem requires a "smooth" weight function, and the underlying distribution function must not have "too much weight in the tails." The distribution function need not be continuous.
Publié le : 1977-12-14
Classification:
Linear combinations of order statistics,
order of normal approximation,
62G30,
62E20
@article{1176995662,
author = {Helmers, R.},
title = {The Order of the Normal Approximation for Linear Combinations of Order Statistics with Smooth Weight Functions},
journal = {Ann. Probab.},
volume = {5},
number = {6},
year = {1977},
pages = { 940-953},
language = {en},
url = {http://dml.mathdoc.fr/item/1176995662}
}
Helmers, R. The Order of the Normal Approximation for Linear Combinations of Order Statistics with Smooth Weight Functions. Ann. Probab., Tome 5 (1977) no. 6, pp. 940-953. http://gdmltest.u-ga.fr/item/1176995662/