A new tail bound for the sum of bounded independent random variables
Probability
2025-03-25 v1 Statistics Theory
Statistics Theory
Abstract
We construct a new tail bound for the sum of independent random variables for situations in which the expected value of the sum is known and each random variable lies within a specified interval, which may be different for each variable. This new bound can be computed by solving a two-dimensional convex optimization problem. Simulations demonstrate that the new bound is often substantially tighter than Hoeffding's inequality for cases in which both bounds are applicable.
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Cite
@article{arxiv.2503.17594,
title = {A new tail bound for the sum of bounded independent random variables},
author = {Jackson Loper and Jeffrey Regier},
journal= {arXiv preprint arXiv:2503.17594},
year = {2025}
}
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