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.
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