Title: Sharpening Jensen's Inequality,
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.