Berry-Esseen bounds in the Breuer-Major CLT and Gebelein's inequality
classification
🧮 math.PR
keywords
approachberry-esseenboundsbreuer-majorgebeleininequalityapproximationsassumptions
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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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