Sharpening Jensen's Inequality

By Jason Liao, Arthur Berg. American Statistician, 2017

91 citations recorded by the source corpus.

Abstract 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.

Subfields: Applied Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/14d89e1b9bdf418df88d19d14a2d7ff48e4c8582

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Statistics and Probability

Citations in the corpus

Bounds on the Jensen Gap, and Implications for Mean-Concentrated Distributions (2017, background): “The result in [13] gives the same upper bound as ours and fall back to Jensen’s inequality for the lower bound.”
Learning deep kernels for exponential family densities (2018, methodology): “Inspired by the technique of Liao and Berg (2018), we will decompose the bias as follows.”
Pushing the bounds of dropout (2018, unknown): “Liao and Berg (2017) show that the Jensen gap E[φ(L)]− φ(E[L]) can be bounded from below and above: inf{h(l;μ) | l ∈ (a, b)} var(L) 6 E[φ(L)]− φ(E[L]) 6 sup{h(l;μ) | l ∈ (a, b)} var(L) (10)”
A Group-Theoretic Framework for Data Augmentation (2019, unknown): “is question is equivalent to characterizing the \Jensen gap": E P[’(f(X)) jX2GX] ’(E P[f(X) jX2GX]): There are some results on lower bounding the Jensen gap under such full generality (see, e.g.,Liao and Berg 2018and references therein). To fully characterize the gap, it is necessary to do a ca”