Chernoff's density is log-concave

We show that the density of = argmax{ - }, sometimes known as Chernoff's density, is log-concave. We conjecture that Chernoff's density is strongly log-concave or "super-Gaussian", and provide evidence in support of the conjecture.

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Bibliographic Details
Published inBernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability Vol. 20; no. 1; p. 231
Main Authors Balabdaoui, Fadoua, Wellner, Jon A
Format Journal Article
LanguageEnglish
Published England 01.02.2014
Subjects
Brownian motion
Polya frequency function
monotone function estimation
slope process
airy function
strongly log-concave
log-concave
Schoenberg’s theorem
Prekopa–Leindler theorem
correlation inequalities
hyperbolically monotone
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Summary:We show that the density of = argmax{ - }, sometimes known as Chernoff's density, is log-concave. We conjecture that Chernoff's density is strongly log-concave or "super-Gaussian", and provide evidence in support of the conjecture.
ISSN:1350-7265
DOI:10.3150/12-BEJ483