Tusnady's inequality revisited

• 成果类型: Article
• 署名作者: Carter, A; Pollard, D
• 署名单位: University of California System; University of California Santa Barbara; Yale University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053604000000733
• 发表日期: 2004
• 页码: 2731-2741
• 关键词: binomial f beta; normal approximation; DENSITY-ESTIMATION; EQUIVALENCE

摘要

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.