A Berry–Esseen bound of order $\protect \frac{1}{\protect \sqrt{n}} $ for martingales
- Resource Type
- article
- Authors
- Wu, Songqi; Ma, Xiaohui; Sang, Hailin; Fan, Xiequan
- Source
- Comptes Rendus. Mathématique, Vol 358, Iss 6, Pp 701-712 (2020)
- Subject
- Mathematics
QA1-939
- Language
- English
French
- ISSN
- 1778-3569
Renz [13] 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 [2] and Grama and Haeusler [6], is applied for obtaining the same convergence rate for a class of more general martingales. An application to linear processes is discussed.