Gaussian martingale inequality applies to random functions and maxima of empirical processes

Xiequan Fan

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arXiv · 1706.03916

Gaussian martingale inequality applies to random functions and maxima of empirical processes

Xiequan Fan

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Abstract

We obtain a Bernstein type Gaussian concentration inequality for martingales. Our inequality improves the Azuma-Hoeffding inequality for moderate deviations $x$. 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.

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Xiequan Fan. 2017-06-13. Gaussian martingale inequality applies to random functions and maxima of empirical processes. https://arxiv.org/abs/1706.03916

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