Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 18 (2013), paper no. 7, 14 pp.
Stein's density approach and information inequalities
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.
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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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