Emergent Mind
A concavity property for the reciprocal of Fisher information and its consequences on Costa's EPI
(1410.2722)
Published Oct 10, 2014
in
cs.IT
,
math-ph
,
math.IT
,
and
math.MP
Abstract
We prove that the reciprocal of Fisher information of a log-concave probability density $X$ in ${\bf{R}}n$ 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 ${\bf{R}}n$ is nonnegative in $t$ with respect to the addition of a Gaussian noise $Z_t$. For log-concave densities this improves the well-known Costa's concavity property of the entropy power.
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