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May 2007 Normal approximation for nonlinear statistics using a concentration inequality approach
Louis H.Y. Chen, Qi-Man Shao
Bernoulli 13(2): 581-599 (May 2007). DOI: 10.3150/07-BEJ5164


Let $T$ be a general sampling statistic that can be written as a linear statistic plus an error term. Uniform and non-uniform Berry–Esseen type bounds for $T$ are obtained. The bounds are the best possible for many known statistics. Applications to U-statistics, multisample U-statistics, L-statistics, random sums and functions of nonlinear statistics are discussed.


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Louis H.Y. Chen. Qi-Man Shao. "Normal approximation for nonlinear statistics using a concentration inequality approach." Bernoulli 13 (2) 581 - 599, May 2007.


Published: May 2007
First available in Project Euclid: 18 May 2007

zbMATH: 1146.62310
MathSciNet: MR2331265
Digital Object Identifier: 10.3150/07-BEJ5164

Keywords: concentration inequality approach , L-statistics , multisample U-statistics , nonlinear statistics , non-uniform Berry–Esseen bound , Normal approximation , uniform Berry–Esseen bound , U-statistics

Rights: Copyright © 2007 Bernoulli Society for Mathematical Statistics and Probability


Vol.13 • No. 2 • May 2007
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