Gaussian martingale inequality applies to random functions and maxima of empirical processes
Probability
2017-10-17 v2
Abstract
We obtain a Bernstein type Gaussian concentration inequality for martingales. Our inequality improves the Azuma-Hoeffding inequality for moderate deviations . Following the work of McDiarmid (1989), Talagrand (1996) and Boucheron, Lugosi and Massart (2000,2003), we show that our result can be applied to the concentration of random functions, Erd\"{o}s-R\'{e}nyi random graph, and maxima of empirical processes. Several interesting Gaussian concentration inequalities have been obtained.
Keywords
Cite
@article{arxiv.1706.03916,
title = {Gaussian martingale inequality applies to random functions and maxima of empirical processes},
author = {Xiequan Fan},
journal= {arXiv preprint arXiv:1706.03916},
year = {2017}
}
Comments
25 pages