## Bernoulli

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

### Normal approximation for nonlinear statistics using a concentration inequality approach

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 18 May 2007

https://projecteuclid.org/euclid.bj/1179498762

Digital Object Identifier
doi:10.3150/07-BEJ5164

Mathematical Reviews number (MathSciNet)
MR2331265

Zentralblatt MATH identifier
1146.62310

#### Citation

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. https://projecteuclid.org/euclid.bj/1179498762

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