Strengthened Chernoff-type variance bounds

TL;DR

This paper develops a new class of strengthened Chernoff-type variance bounds for absolutely continuous random variables within the integrated Pearson family, leveraging orthonormal polynomial properties.

Contribution

It introduces novel variance bounds that extend classical Chernoff bounds using orthogonal polynomial techniques for a specific family of distributions.

Findings

New class of variance bounds derived

Bounds applicable to integrated Pearson family

Enhanced bounds compared to classical Chernoff bounds

Abstract

Let $X$ be an absolutely continuous random variable from the integrated Pearson family and assume that $X$ has finite moments of any order. Using some properties of the associated orthonormal polynomial system, we provide a class of strengthened Chernoff-type variance bounds.