Bernstein-Type Bounds for Beta Distribution

TL;DR

This paper derives sharp Bernstein-type concentration inequalities for the beta distribution, improving existing bounds by leveraging a new recursion for central moments based on hypergeometric representations.

Contribution

Introduces a novel recursion for beta distribution moments, enabling explicit tail bounds and sharper concentration inequalities.

Findings

Sharp Bernstein-type bounds for beta distribution

New recursion for central moments using hypergeometric functions

Improved tail approximations for beta distribution

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.