Tusnády’s inequality revisited
| Autor: | David Pollard, Andrew V. Carter |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2004 |
| Předmět: |
Statistics and Probability
Binomial (polynomial) Modulo Quantile coupling equivalent normal deviate Mathematics - Statistics Theory Statistics Theory (math.ST) symbols.namesake Tusnády’s inequality Simple (abstract algebra) Elementary proof Taylor series FOS: Mathematics Mathematics Discrete mathematics beta integral representation of Binomial tails Brownian bridge Coupling (probability) Empirical distribution function KMT/Hungarian construction 62E17 (Primary) 62B15. (Secondary) ratios of normal tails symbols 62E17 Statistics Probability and Uncertainty 62B15 |
| Zdroj: | Ann. Statist. 32, no. 6 (2004), 2731-2741 |
| Popis: | 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. Comment: Published at http://dx.doi.org/10.1214/009053604000000733 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org) |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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