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Berry-Esseen bounds in the Breuer-Major CLT and Gebelein's inequality (1812.08838v2)
Published 20 Dec 2018 in math.PR
Abstract: We derive explicit Berry-Esseen bounds in the total variation distance for the Breuer-Major central limit theorem, in the case of a subordinating function $\varphi$ satisfying minimal regularity assumptions. Our approach is based on the combination of the Malliavin-Stein approach for normal approximations with Gebelein's inequality, bounding the covariance of functionals of Gaussian fields in terms of maximal correlation coefficients.
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