English

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 xx. 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}
}

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25 pages