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arXiv · 2003.03197

Bounding probability of small deviation on sum of independent random variables: Combination of moment approach and Berry-Esseen theorem

Jiayi Guo·Simai He·Zi Ling·Yicheng Liu
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Abstract

In the context of bounding probability of small deviation, there are limited general tools. However, such bounds have been widely applied in graph theory and inventory management. We introduce a common approach to substantially sharpen such inequality bounds by combining the semidefinite optimization approach of moments problem and the Berry-Esseen theorem. As an application, we improve the lower bound of Feige's conjecture from 0.14 to 0.1798.

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Jiayi Guo, Simai He, Zi Ling, Yicheng Liu. 2020-03-06. Bounding probability of small deviation on sum of independent random variables: Combination of moment approach and Berry-Esseen theorem. https://arxiv.org/abs/2003.03197

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