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Berry-Esseen Bounds for Statistics of Weakly Dependent Samples

V. Bentkus, F. Götze and A. Tikhomirov
Bernoulli
Vol. 3, No. 3 (Sep., 1997), pp. 329-349
DOI: 10.2307/3318596
Stable URL: http://www.jstor.org/stable/3318596
Page Count: 21
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Berry-Esseen Bounds for Statistics of Weakly Dependent Samples
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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-1/2 logδ N) for U-statistics, studentized means, functions of sample means, functionals of empirical distribution functions and linear combinations of order statistics.

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