Rates of convergence for minimal distances in the central limit theorem under projective criteria

TL;DR

This paper provides estimates of the rates at which the distribution of normalized sums converges to a Gaussian distribution for certain stationary sequences, with applications to linear processes and expanding maps.

Contribution

It introduces new bounds on minimal distances in the central limit theorem for stationary sequences satisfying projective criteria, extending previous results.

Findings

Derived explicit convergence rate estimates for stationary martingale difference sequences

Applied results to functions of linear processes and expanding maps

Enhanced understanding of distributional approximations in dependent sequences

Abstract

In this paper, we give estimates of ideal or minimal distances between the distribution of the normalized partial sum and the limiting Gaussian distribution for stationary martingale difference sequences or stationary sequences satisfying projective criteria. Applications to functions of linear processes and to functions of expanding maps of the interval are given.