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arXiv · 1812.08838

Berry-Esseen bounds in the Breuer-Major CLT and Gebelein's inequality

Ivan Nourdin·Giovanni Peccati·Xiaochuan Yang
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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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Ivan Nourdin, Giovanni Peccati, Xiaochuan Yang. 2018-12-20. Berry-Esseen bounds in the Breuer-Major CLT and Gebelein's inequality. https://arxiv.org/abs/1812.08838

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