A Berry-Esseen bound with (almost) sharp dependence conditions
نویسندگان
چکیده
Suppose that the (normalised) partial sum of a stationary sequence converges to standard normal random variable. Given sufficiently moments, when do we have rate convergence n−1∕2 in uniform metric, other words, optimal Berry-Esseen bound? We study this question quite general framework and find (almost) sharp dependence conditions. The result applies many different processes dynamical systems. As specific, prominent examples, functions doubling map 2x mod 1, left walk on linear group processes.
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ژورنال
عنوان ژورنال: Bernoulli
سال: 2023
ISSN: ['1573-9759', '1350-7265']
DOI: https://doi.org/10.3150/22-bej1496