Electronic Communications in Probability

Stein's density approach and information inequalities

Christophe Ley and Yvik Swan

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We provide a new perspective on Stein's so-called density approach by introducing a new operator and characterizing class which are valid for a much wider family of probability distributions on the real line. We prove an elementary factorization property of this operator and propose a new Stein identity which we use to derive information inequalities in terms of what we call the "generalized Fisher information distance". We provide explicit bounds on the constants appearing in these inequalities for several important cases. We conclude with a comparison between our results and known results in the Gaussian case, hereby improving on several known inequalities from the literature.

Article information

Electron. Commun. Probab., Volume 18 (2013), paper no. 7, 14 pp.

Accepted: 27 January 2013
First available in Project Euclid: 7 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60F05: Central limit and other weak theorems
Secondary: 94A17: Measures of information, entropy

generalized Fisher information magic factors Pinsker's inequality probability metrics Stein's density approach

This work is licensed under a Creative Commons Attribution 3.0 License.


Ley, Christophe; Swan, Yvik. Stein's density approach and information inequalities. Electron. Commun. Probab. 18 (2013), paper no. 7, 14 pp. doi:10.1214/ECP.v18-2578. https://projecteuclid.org/euclid.ecp/1465315546

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