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Multivariate Poisson-binomial approximation using Stein‘s method


Barbour, A D (2005). Multivariate Poisson-binomial approximation using Stein‘s method. In: Barbour, A D; Chen, L H Y. Stein‘s method and applications. Singapore: Singapore Univ. Press, 131-142.

Abstract

The paper is concerned with the accuracy in total variation of the approximation of the distribution of a sum of independent Bernoulli distributed random d–vectors by the product distribution with Poisson marginals which has the same mean. The best results, obtained using generating function methods, are those of Roos (1998, 1999). Stein's method has so far yielded somewhat weaker bounds. We demonstrate why a direct approach using Stein's method cannot emulate Roos's results, but give some less direct arguments to show that it is possible, using Stein's method, to get very close.

Abstract

The paper is concerned with the accuracy in total variation of the approximation of the distribution of a sum of independent Bernoulli distributed random d–vectors by the product distribution with Poisson marginals which has the same mean. The best results, obtained using generating function methods, are those of Roos (1998, 1999). Stein's method has so far yielded somewhat weaker bounds. We demonstrate why a direct approach using Stein's method cannot emulate Roos's results, but give some less direct arguments to show that it is possible, using Stein's method, to get very close.

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Additional indexing

Item Type:Book Section, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2005
Deposited On:10 Nov 2009 07:39
Last Modified:05 Apr 2016 13:24
Publisher:Singapore Univ. Press
Series Name:Lecture Notes Series Institute for Mathematical Sciences, National University of Singapore
Number:5
ISSN:1793-0758
ISBN:981-256-281-8
Additional Information:Electronic version of an article published as Lecture Notes Series. Institute for Mathematical Sciences. National University of Singapore, 5. Published jointly by Singapore University Press, Singapore; and World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2005. xx+297 pp © 2005 copyright World Scientific Publishing Company
Official URL:http://ebooks.worldscinet.com/ISBN/9789812567673/9789812567673_0008.html

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