Mathematics > Probability
[Submitted on 20 Dec 2018 (v1), last revised 8 May 2019 (this version, v2)]
Title:Berry-Esseen bounds in the Breuer-Major CLT and Gebelein's inequality
View PDFAbstract: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.
Submission history
From: Xiaochuan Yang [view email][v1] Thu, 20 Dec 2018 21:04:12 UTC (14 KB)
[v2] Wed, 8 May 2019 02:57:09 UTC (15 KB)
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