• Bernoulli
  • Volume 13, Number 2 (2007), 581-599.

Normal approximation for nonlinear statistics using a concentration inequality approach

Louis H.Y. Chen and Qi-Man Shao

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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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Bernoulli, Volume 13, Number 2 (2007), 581-599.

First available in Project Euclid: 18 May 2007

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concentration inequality approach L-statistics multisample U-statistics non-uniform Berry–Esseen bound nonlinear statistics normal approximation U-statistics uniform Berry–Esseen bound


Chen, Louis H.Y.; Shao, Qi-Man. Normal approximation for nonlinear statistics using a concentration inequality approach. Bernoulli 13 (2007), no. 2, 581--599. doi:10.3150/07-BEJ5164.

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