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arXiv · 2002.00307

A Berry-Esseen bound of order $ 1/\sqrt{n} $ for martingales

Songqi Wu·Xiaohui Ma·Hailin Sang·Xiequan Fan
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Abstract

Renz (Ann. Probab. 1996) has established a rate of convergence $1/\sqrt{n}$ 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.

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Songqi Wu, Xiaohui Ma, Hailin Sang, Xiequan Fan. 2020-02-02. A Berry-Esseen bound of order $ 1/\sqrt{n} $ for martingales. https://arxiv.org/abs/2002.00307

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