Permanent URL to this publication: http://dx.doi.org/10.5167/uzh38381
Barbour, A D; Johnson, O; Kontoyiannis, I; Madiman, M (2010). Compound poisson approximation via information functionals. Electronic Journal of Probability, 15(42):13441369.

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Abstract
An informationtheoretic development is given for the problem of compound Poisson approximation, which parallels earlier treatments for Gaussian and Poisson approximation. Nonasymptotic bounds are derived for the distance between the distribution of a sum of independent integervalued random variables and an appropriately chosen compound Poisson law. In the case where all summands have the same conditional distribution given that they are nonzero, a bound on the relative entropy distance between their sum and the compound Poisson distribution is derived, based on the dataprocessing property of relative entropy and earlier Poisson approximation results. When the summands have arbitrary distributions, corresponding bounds are derived in terms of the total variation distance. The main technical ingredient is the introduction of two "information functionals,'' and the analysis of their properties. These information functionals play a role analogous to that of the classical Fisher information in normal approximation. Detailed comparisons are made between the resulting inequalities and related bounds.
Item Type:  Journal Article, refereed, original work 

Communities & Collections:  07 Faculty of Science > Institute of Mathematics 
DDC:  510 Mathematics 
Language:  English 
Date:  31 August 2010 
Deposited On:  23 Dec 2010 13:53 
Last Modified:  27 Nov 2013 21:30 
Publisher:  Institute of Mathematical Statistics 
ISSN:  10836489 
Official URL:  http://www.math.washington.edu/~ejpecp/EjpVol15/paper42.abs.html 
Related URLs:  http://arxiv.org/abs/1004.3692 
Citations:  Web of Science®. Times Cited: 10 Google Scholar™ Scopus®. Citation Count: 12 
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