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Thinning, entropy, and the law of thin numbers

Harremoës, P and Johnson, O and Kontoyiannis, I (2010) Thinning, entropy, and the law of thin numbers. IEEE Transactions on Information Theory, 56. pp. 4228-4244. ISSN 0018-9448

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Abstract

Rnyi's thinning operation on a discrete random variable is a natural discrete analog of the scaling operation for continuous random variables. The properties of thinning are investigated in an information-theoretic context, especially in connection with information-theoretic inequalities related to Poisson approximation results. The classical Binomial-to-Poisson convergence (sometimes referred to as the law of small numbers) is seen to be a special case of a thinning limit theorem for convolutions of discrete distributions. A rate of convergence is provided for this limit, and nonasymptotic bounds are also established. This development parallels, in part, the development of Gaussian inequalities leading to the information-theoretic version of the central limit theorem. In particular, a thinning Markov chain is introduced, and it is shown to play a role analogous to that of the Ornstein-Uhlenbeck process in connection to the entropy power inequality. © 2010 IEEE.

Item Type: Article
Subjects: UNSPECIFIED
Divisions: Div F > Signal Processing and Communications
Depositing User: Cron Job
Date Deposited: 08 Jan 2018 20:10
Last Modified: 27 Oct 2020 07:12
DOI: 10.1109/TIT.2010.2053893