Asymptotic normality of linear combinations of order statistics of the form $T_n = n^{-1} \sum J(i/(n + 1))X_{in}$ is investigated along with a slightly trimmed version of $T_n$. Theorem 5 of Stigler (1974) is extended to show asymptotic normality of $T_n$ for a wide class of score functions. In addition, a proof of Theorem 4 of Stigler (1974) is given.
Publié le : 1981-07-14
Classification:
Linear combinations of order statistics,
asymptotic normality,
efficient estimation,
62G30,
60F05,
62E20,
63G35
@article{1176345531,
author = {Mason, David M.},
title = {Asymptotic Normality of Linear Combinations of Order Statistics with a Smooth Score Function},
journal = {Ann. Statist.},
volume = {9},
number = {1},
year = {1981},
pages = { 899-908},
language = {en},
url = {http://dml.mathdoc.fr/item/1176345531}
}
Mason, David M. Asymptotic Normality of Linear Combinations of Order Statistics with a Smooth Score Function. Ann. Statist., Tome 9 (1981) no. 1, pp. 899-908. http://gdmltest.u-ga.fr/item/1176345531/