A Berry-Esseen bound of order $ 1/\sqrt{n} $ for martingales
Probability
2020-02-04 v1
Abstract
Renz (Ann. Probab. 1996) has established a rate of convergence in the central limit theorem for martingales with some restrictive conditions. In the present paper a modification of the methods, developed by Bolthausen (Ann. Probab. 1982) and Grama and Haeusler (Stochastic Process. Appl. 2000), is applied for obtaining the same convergence rate for a class of more general martingales. An application to linear processes is discussed.
Cite
@article{arxiv.2002.00307,
title = {A Berry-Esseen bound of order $ 1/\sqrt{n} $ for martingales},
author = {Songqi Wu and Xiaohui Ma and Hailin Sang and Xiequan Fan},
journal= {arXiv preprint arXiv:2002.00307},
year = {2020}
}