Berry-Esseen bounds in the Breuer-Major CLT and Gebelein's inequality
Ivan Nourdin, Giovanni Peccati, Xiaochuan Yang · arXiv (Cornell University) · 2018
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 $φ$ 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.