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arXiv · 1105.2550

A Maximal Large Deviation Inequality for Sub-Gaussian Variables

Dotan Di Castro·Claudio Gentile·Shie Mannor
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Abstract

In this short note we prove a maximal concentration lemma for sub-Gaussian random variables stating that for independent sub-Gaussian random variables we have \[P<(\max_{1\le i\le N}S_{i}>\epsilon>) \le\exp<(-\frac{1}{N^2}\sum_{i=1}^{N}\frac{\epsilon^{2}}{2\sigma_{i}^{2}}>), \] where $S_i$ is the sum of $i$ zero mean independent sub-Gaussian random variables and $\sigma_i$ is the variance of the $i$th random variable.

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Dotan Di Castro, Claudio Gentile, Shie Mannor. 2011-05-12. A Maximal Large Deviation Inequality for Sub-Gaussian Variables. https://arxiv.org/abs/1105.2550

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