We prove that the reciprocal of Fisher information of a logconcave probability density is concave in t with respect to the addition of a Gaussian noise of variance t. As a byproduct of this result we show that the third derivative of the entropy power of a log-concave probability density is nonnegative in t with respect to the addition of a Gaussian noise of variance t. For log-concave densities this improves the well-known Costa’s concavity property of the entropy power.
A concavity property for the reciprocal of Fisher information and its consequences on Costa's EPI
TOSCANI, GIUSEPPE
2015-01-01
Abstract
We prove that the reciprocal of Fisher information of a logconcave probability density is concave in t with respect to the addition of a Gaussian noise of variance t. As a byproduct of this result we show that the third derivative of the entropy power of a log-concave probability density is nonnegative in t with respect to the addition of a Gaussian noise of variance t. For log-concave densities this improves the well-known Costa’s concavity property of the entropy power.File in questo prodotto:
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