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arXiv · 0708.4272

Normal approximation for nonlinear statistics using a concentration inequality approach

Louis H. Y. Chen·Qi-Man Shao
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Abstract

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. 2007-08-31. Normal approximation for nonlinear statistics using a concentration inequality approach. https://doi.org/10.3150/07-bej5164

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