New insights on concentration inequalities for self-normalized martingales
Probability
2019-06-17 v2
Abstract
We propose new concentration inequalities for self-normalized martingales. The main idea is to introduce a suitable weighted sum of the predictable quadratic variation and the total quadratic variation of the martingale. It offers much more flexibility and allows us to improve previous concentration inequalities. Statistical applications on autoregressive process, internal diffusion-limited aggregation process, and online statistical learning are also provided.
Keywords
Cite
@article{arxiv.1810.10590,
title = {New insights on concentration inequalities for self-normalized martingales},
author = {Bernard Bercu and Taieb Touati},
journal= {arXiv preprint arXiv:1810.10590},
year = {2019}
}
Comments
17 pages, Motivation has been better presented, Improvement of Corollary 3.3, typos have been corrected