An almost sure invariance principle for Kolmogorov-Smirnov statistics for vector chance variables is established along the lines of Theorems 1.4 and 4.9 of Strassen [Proc. Fifth Berkeley Symp. Math. Statist. Prob. (1967) 2 315-343]. This strengthens certain asymptotic expressions on the probability of moderate deviations for Kolmogorov-Smirnov statistics, obtained earlier by Gnedenko, Karoluk and Skorokhod, and by Kiefer and Wolfowitz, among others.
Publié le : 1973-06-14
Classification:
Almost sure invariance principle,
multivariate Kolmogorov-Smirnov statistics,
probability of moderate deviations,
reverse sub-martingales,
60B10,
60F15,
62E20
@article{1176996943,
author = {Sen, Pranab Kumar},
title = {An Almost Sure Invariance Principle for Mutivariate Kolmogorov-Smirnov Statistics},
journal = {Ann. Probab.},
volume = {1},
number = {5},
year = {1973},
pages = { 488-496},
language = {en},
url = {http://dml.mathdoc.fr/item/1176996943}
}
Sen, Pranab Kumar. An Almost Sure Invariance Principle for Mutivariate Kolmogorov-Smirnov Statistics. Ann. Probab., Tome 1 (1973) no. 5, pp. 488-496. http://gdmltest.u-ga.fr/item/1176996943/