Sharpening Jensen's Inequality

TL;DR

This paper introduces a new, simple, and broadly applicable sharpened Jensen's inequality that enhances existing bounds and has diverse applications in statistics and mathematical analysis.

Contribution

It proposes a novel sharpened Jensen's inequality that is easy to apply, requires minimal assumptions, and improves upon traditional bounds.

Findings

The new inequality provides more accurate bounds in various applications.

It is simple to incorporate into calculus-based statistical courses.

Applications include moment generating functions, power mean inequalities, and Rao-Blackwell estimation.

Abstract

This paper proposes a new sharpened version of the Jensen's inequality. The proposed new bound is simple and insightful, is broadly applicable by imposing minimum assumptions, and provides fairly accurate result in spite of its simple form. Applications to the moment generating function, power mean inequalities, and Rao-Blackwell estimation are presented. This presentation can be incorporated in any calculus-based statistical course.