EJP Reading Tools

Compound Poisson Approximation via Information Functionals

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Compound Poisson Approximation via Information Functionals
2.	Creator	Author's name, affiliation, country	A. D. Barbour; Universität Zürich; Switzerland
2.	Creator	Author's name, affiliation, country	Oliver Johnson; University of Bristol; United Kingdom
2.	Creator	Author's name, affiliation, country	Ioannis Kontoyiannis; Athens University of Economics & Business; Greece
2.	Creator	Author's name, affiliation, country	Mokshay Madiman; Yale University; United States
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Compound Poisson approximation, Fisher information, information theory, relative entropy, Stein's method
3.	Subject	Subject classification	60E15; 60E07; 60F05; 94A17
4.	Description	Abstract	An information-theoretic 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 integer-valued random variables and an appropriately chosen compound Poisson law. In the case where all summands have the same conditional distribution given that they are non-zero, a bound on the relative entropy distance between their sum and the compound Poisson distribution is derived, based on the data-processing 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.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	I.K. was supported in part by a Marie Curie International Outgoing Fellowship, PIOF-GA-2009-235837.
7.	Date	(YYYY-MM-DD)	2010-08-31
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/799
10.	Identifier	Digital Object Identifier	10.1214/EJP.v15-799
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 15
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
15.	Rights	Copyright and permissions	The Electronic Journal of Probability applies the Creative Commons Attribution License (CCAL) to all articles we publish in this journal. Under the CCAL, authors retain ownership of the copyright for their article, but authors allow anyone to download, reuse, reprint, modify, distribute, and/or copy articles published in EJP, so long as the original authors and source are credited. This broad license was developed to facilitate open access to, and free use of, original works of all types. Applying this standard license to your work will ensure your right to make your work freely and openly available. Summary of the Creative Commons Attribution License You are free to copy, distribute, display, and perform the work to make derivative works to make commercial use of the work under the following condition of Attribution: others must attribute the work if displayed on the web or stored in any electronic archive by making a link back to the website of EJP via its Digital Object Identifier (DOI), or if published in other media by acknowledging prior publication in this Journal with a precise citation including the DOI. For any further reuse or distribution, the same terms apply. Any of these conditions can be waived by permission of the Corresponding Author.