A strengthened version of the Glivenko-Cantelli theorem for the uniform empirical distribution function is proved. The strengthened Glivenko-Cantelli theorem is used to establish strong laws of large numbers for linear functions of order statistics.
Publié le : 1977-05-14
Classification:
Glivenko-Cantelli theorem,
order statistics,
strong laws of large numbers,
60F15,
62G30
@article{1176343844,
author = {Wellner, Jon A.},
title = {A Glivenko-Cantelli Theorem and Strong Laws of Large Numbers for Functions of Order Statistics},
journal = {Ann. Statist.},
volume = {5},
number = {1},
year = {1977},
pages = { 473-480},
language = {en},
url = {http://dml.mathdoc.fr/item/1176343844}
}
Wellner, Jon A. A Glivenko-Cantelli Theorem and Strong Laws of Large Numbers for Functions of Order Statistics. Ann. Statist., Tome 5 (1977) no. 1, pp. 473-480. http://gdmltest.u-ga.fr/item/1176343844/