The functional $T(F) = \int F^{-1}(t)J(t) dt$ associated with linear combinations of order statistics is shown to have a Frechet-type differential. As a corollary, the statistic $T(F_n)$ obtained by evaluating $T(\cdot)$ at the sample df $F_n$ is seen to be asymptotically normal and to obey a law of the iterated logarithm.
Publié le : 1979-09-14
Classification:
Differential,
linear combinations of order statistics,
asymptotic normality,
law of the iterated logarithm,
62E20,
62G30
@article{1176344781,
author = {Boos, Dennis D.},
title = {A Differential for $L$-Statistics},
journal = {Ann. Statist.},
volume = {7},
number = {1},
year = {1979},
pages = { 955-959},
language = {en},
url = {http://dml.mathdoc.fr/item/1176344781}
}
Boos, Dennis D. A Differential for $L$-Statistics. Ann. Statist., Tome 7 (1979) no. 1, pp. 955-959. http://gdmltest.u-ga.fr/item/1176344781/