The Annals of Statistics

Tusnády’s inequality revisited

Andrew Carter and David Pollard

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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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Ann. Statist., Volume 32, Number 6 (2004), 2731-2741.

First available in Project Euclid: 7 February 2005

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Zentralblatt MATH identifier

Primary: 62E17: Approximations to distributions (nonasymptotic)
Secondary: 62B15: Theory of statistical experiments

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


Carter, Andrew; Pollard, David. Tusnády’s inequality revisited. Ann. Statist. 32 (2004), no. 6, 2731--2741. doi:10.1214/009053604000000733.

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