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Self-normalized Cramer type moderate deviations for martingales
- Source :
- Bernoulli 25, No. 4A. (2019), 2793-2823
- Publication Year :
- 2017
-
Abstract
- Let $(\xi_i,\mathcal{F}_i)_{i\geq1}$ be a sequence of martingale differences. Set $S_n=\sum_{i=1}^n\xi_i $ and $[ S]_n=\sum_{i=1}^n \xi_i^2.$ We prove a Cram\'er type moderate deviation expansion for $\mathbf{P}(S_n/\sqrt{[ S]_n} \geq x)$ as $n\to+\infty.$ Our results partly extend the earlier work of [Jing, Shao and Wang, 2003] for independent random variables.
- Subjects :
- Mathematics - Probability
Subjects
Details
- Database :
- arXiv
- Journal :
- Bernoulli 25, No. 4A. (2019), 2793-2823
- Publication Type :
- Report
- Accession number :
- edsarx.1712.04756
- Document Type :
- Working Paper