Bernstein-Type Bounds for Beta Distribution
Probability
2024-10-21 v5 Statistics Theory
Applications
Statistics Theory
Abstract
This work obtains sharp closed-form exponential concentration inequalities of Bernstein type for the ubiquitous beta distribution, improving upon sub-gaussian and sub-gamma bounds previously studied in this context. The proof leverages a novel handy recursion of order 2 for central moments of the beta distribution, obtained from the hypergeometric representations of moments; this recursion is useful for obtaining explicit expressions for central moments and various tail approximations.
Cite
@article{arxiv.2101.02094,
title = {Bernstein-Type Bounds for Beta Distribution},
author = {Maciej Skorski},
journal= {arXiv preprint arXiv:2101.02094},
year = {2024}
}
Comments
major revision - fixed a mistake in the proof