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

[摘要] 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 $ arphi $ 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.

[学科分类] 统计和概率

[关键词] Breuer-Major theorem;rate of convergence;Gebelein’s inequality;Malliavin-Stein approach