Bernstein-Type Bounds for Beta Distribution
arXiv:2101.02094 · doi:10.15559/23-VMSTA223
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.
major revision - fixed a mistake in the proof