A concavity property for the reciprocal of Fisher information and its consequences on Costa’s EPI

Giuseppe Toscani

Physica A: Statistical Mechanics and its Applications, 2015, vol. 432, issue C, 35-42

Abstract: We prove that the reciprocal of Fisher information of a log-concave probability density X in Rn is concave in t with respect to the addition of a Gaussian noise Zt=N(0,tIn). As a byproduct of this result we show that the third derivative of the entropy power of a log-concave probability density X in Rn is nonnegative in t with respect to the addition of a Gaussian noise Zt. For log-concave densities this improves the well-known Costa’s concavity property of the entropy power (Costa, 1985).

Keywords: Entropy-power inequality; Blachman–Stam inequality; Costa’s concavity property; Fisher information; Log-concave functions (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:432:y:2015:i:c:p:35-42

DOI: 10.1016/j.physa.2015.03.018

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