Inequalities for characteristic functions involving Fisher information
type: Item
instance of: scholarly article
title: Inequalities for characteristic functions involving Fisher information
zbMATH Open document ID: 1143.62001
author: Zhengmin Zhang
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2007-04-13T00:00:00Z
review text: Let \(f(x)\) be a one-dimensional probability density with characteristic function \(\phi(t)\). The author gives several estimates from above for \(\text{Re } \phi(t)\), \(\text{Im } \phi(t)\) and \(| \phi(t)| ^2\) in terms of the Fisher information \(I(f):=\int ((d/dx)\ln f(x))^2 f(x)\, dx\). In particular, the estimate \(| \phi(t)| ^2\leq I(f)/(I(f)+t^2)\), \(t\in R\), holds.
Mathematics Subject Classification ID: 62B10
Mathematics Subject Classification ID: 60E10
Mathematics Subject Classification ID: 60E15
Mathematics Subject Classification ID: 42A61
zbMATH DE Number: 5142257
zbMATH Keywords: characteristic function
zbMATH Keywords: Fourier transform
zbMATH Keywords: Fisher information
reviewed by: Ilya Pavlyukevich
MaRDI profile type: Publication
full work available at URL: j.crma.2007.01.008
OpenAlex ID: W1972385663
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DOI: 10.1016/J.CRMA.2007.01.008
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description: scientific article; zbMATH DE number 5142257