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2019 Berry-Esseen bounds in the Breuer-Major CLT and Gebelein’s inequality
Ivan Nourdin, Giovanni Peccati, Xiaochuan Yang
Electron. Commun. Probab. 24: 1-12 (2019). DOI: 10.1214/19-ECP241

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.

Citation

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Ivan Nourdin. Giovanni Peccati. Xiaochuan Yang. "Berry-Esseen bounds in the Breuer-Major CLT and Gebelein’s inequality." Electron. Commun. Probab. 24 1 - 12, 2019. https://doi.org/10.1214/19-ECP241

Information

Received: 10 February 2019; Accepted: 10 May 2019; Published: 2019
First available in Project Euclid: 22 June 2019

zbMATH: 07088975
MathSciNet: MR3978683
Digital Object Identifier: 10.1214/19-ECP241

Subjects:
Primary: 60F05, 60G15, 60H07

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