Bernoulli

  • 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

Full-text: Open access

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

Permanent link to this document
https://projecteuclid.org/euclid.bj/1179498762

Digital Object Identifier
doi:10.3150/07-BEJ5164

Mathematical Reviews number (MathSciNet)
MR2331265

Zentralblatt MATH identifier
1146.62310

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

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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