Bernoulli

  • Bernoulli
  • Volume 3, Number 3 (1997), 329-349.

Berry-Esseen bounds for statistics of weakly dependent samples

V. Bentkus, F. Götze, and A. Tikhomoirov

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Abstract

We prove Berry--Esseen bounds for a general class of asymptotically normal statistics which are functions of N weakly dependent random variables under easily verifiable conditions. In particular, we show, for some δ >0 , the validity of the bound O (N - 1/2log δ N) for U -statistics, studentized means, functions of sample means, functionals of empirical distribution functions and linear combinations of order statistics.

Article information

Source
Bernoulli, Volume 3, Number 3 (1997), 329-349.

Dates
First available in Project Euclid: 23 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.bj/1177334459

Mathematical Reviews number (MathSciNet)
MR1468309

Zentralblatt MATH identifier
1066.62505

Keywords
absolute regularity asymptotically normal statistics Berry-Esseen bounds functionals of empirical distribution functions functions of sample means linear combinations of order statistics mixing studentized means U-statistics weakly dependent random variables

Citation

Bentkus, V.; Götze, F.; Tikhomoirov, A. Berry-Esseen bounds for statistics of weakly dependent samples. Bernoulli 3 (1997), no. 3, 329--349. https://projecteuclid.org/euclid.bj/1177334459


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References

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