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.
"Rates of convergence for minimal distances in the central limit theorem under projective criteria." Electron. J. Probab. 14 978 - 1011, 2009. https://doi.org/10.1214/EJP.v14-648