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December 2004 Tusnády’s inequality revisited
Andrew Carter, David Pollard
Ann. Statist. 32(6): 2731-2741 (December 2004). DOI: 10.1214/009053604000000733


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.


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Andrew Carter. David Pollard. "Tusnády’s inequality revisited." Ann. Statist. 32 (6) 2731 - 2741, December 2004.


Published: December 2004
First available in Project Euclid: 7 February 2005

zbMATH: 1076.62012
MathSciNet: MR2154001
Digital Object Identifier: 10.1214/009053604000000733

Primary: 62E17
Secondary: 62B15

Keywords: beta integral representation of Binomial tails , equivalent normal deviate , KMT/Hungarian construction , Quantile coupling , ratios of normal tails , Tusnády’s inequality

Rights: Copyright © 2004 Institute of Mathematical Statistics

Vol.32 • No. 6 • December 2004
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