Tusnády’s inequality is the key ingredient in the KMT/Hungarian coupling of the empirical distribution function with a Brownian bridge. We present an elementary proof of a result that sharpens the Tusnády inequality, modulo constants. Our method uses the beta integral representation of Binomial tails, simple Taylor expansion and some novel bounds for the ratios of normal tail probabilities.
Publié le : 2004-12-14
Classification:
Quantile coupling,
KMT/Hungarian construction,
Tusnády’s inequality,
beta integral representation of Binomial tails,
ratios of normal tails,
equivalent normal deviate,
62E17,
62B15
@article{1107794885,
author = {Carter, Andrew and Pollard, David},
title = {Tusn\'ady's inequality revisited},
journal = {Ann. Statist.},
volume = {32},
number = {1},
year = {2004},
pages = { 2731-2741},
language = {en},
url = {http://dml.mathdoc.fr/item/1107794885}
}
Carter, Andrew; Pollard, David. Tusnády’s inequality revisited. Ann. Statist., Tome 32 (2004) no. 1, pp. 2731-2741. http://gdmltest.u-ga.fr/item/1107794885/