Sharpening Jensen's Inequality

This article proposes a new sharpened version of Jensen's inequality. The proposed new bound is simple and insightful, is broadly applicable by imposing minimum assumptions, and provides fairly accurate results in spite of its simple form. Applications to the moment generating function, power m...

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Bibliographic Details
Published inThe American statistician Vol. 73; no. 3; pp. 278 - 281
Main Authors Liao, J. G., Berg, Arthur
Format Journal Article
LanguageEnglish
Published Alexandria Taylor & Francis 03.07.2019
American Statistical Association
Subjects
Jensen gap
Power mean inequality
Rao-Blackwell estimator
Regression analysis
Sharpening
Statistical methods
Statistics
Taylor series
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Summary:This article proposes a new sharpened version of Jensen's inequality. The proposed new bound is simple and insightful, is broadly applicable by imposing minimum assumptions, and provides fairly accurate results 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.
ISSN:0003-1305
1537-2731
DOI:10.1080/00031305.2017.1419145