Repository logo
 

Bounding distributional errors via density ratios

Accepted version
Peer-reviewed

Type

Article

Change log

Authors

Dumbgen, Lutz 
Samworth, Richard J 
Wellner, Jon A 

Abstract

We present some new and explicit error bounds for the approximation of distributions. The approximation error is quantified by the maximal density ratio of the distribution Q to be approximated and its proxy P. This non-symmetric measure is more informative than and implies bounds for the total variation distance. Explicit approximation problems include, among others, hypergeometric by binomial distributions, binomial by Poisson distributions, and beta by gamma distributions. In many cases we provide both upper and (matching) lower bounds.

Description

Keywords

Binomial distribution, hypergeometric distribution, Poisson approximation, relative errors, total variation distance

Journal Title

BERNOULLI

Conference Name

Journal ISSN

1350-7265
1573-9759

Volume Title

27

Publisher

Taylor & Francis

Rights

All rights reserved
Sponsorship
Engineering and Physical Sciences Research Council (EP/N031938/1)
Engineering and Physical Sciences Research Council (EP/P031447/1)