Open Access
Translator Disclaimer
February 2014 Chernoff’s density is log-concave
Fadoua Balabdaoui, Jon A. Wellner
Bernoulli 20(1): 231-244 (February 2014). DOI: 10.3150/12-BEJ483

Abstract

We show that the density of $Z=\mathop{\operatorname{argmax}}\{W(t)-t^{2}\}$, 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.

Citation

Download Citation

Fadoua Balabdaoui. Jon A. Wellner. "Chernoff’s density is log-concave." Bernoulli 20 (1) 231 - 244, February 2014. https://doi.org/10.3150/12-BEJ483

Information

Published: February 2014
First available in Project Euclid: 22 January 2014

zbMATH: 1294.60100
MathSciNet: MR3160580
Digital Object Identifier: 10.3150/12-BEJ483

Keywords: Airy function , Brownian motion , Correlation inequalities , hyperbolically monotone , log-concave , monotone function estimation , Polya frequency function , Prekopa–Leindler theorem , Schoenberg’s theorem , slope process , strongly log-concave

Rights: Copyright © 2014 Bernoulli Society for Mathematical Statistics and Probability

JOURNAL ARTICLE
14 PAGES


SHARE
Vol.20 • No. 1 • February 2014
Back to Top