Tusnady's inequality revisited

Details Tusnady's inequality revisited Tusnady's inequality revisited

2005-08-30

arxiv.org/abs/math/0508606v1

Annals of Statistics 2004, Vol. 32, No. 6, 2731-2741

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053604000000733 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053604000000733

Tusnady'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 Tusnady 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.

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