Chernoff's density is log-concave

• Published in: Bernoulli : 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
• Language: English
• 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

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.