Bounding distributional errors via density ratios

Dümbgen, Lutz; Samworth, Richard J.; Wellner, Jon A. (2021). Bounding distributional errors via density ratios. Bernoulli, 27(2), pp. 818-852. International Statistical Institute 10.3150/20-BEJ1256

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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.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science

UniBE Contributor:

Dümbgen, Lutz

Subjects:

500 Science > 510 Mathematics

ISSN:

1350-7265

Publisher:

International Statistical Institute

Funders:

[4] Swiss National Science Foundation

Language:

English

Submitter:

Lutz Dümbgen

Date Deposited:

14 Apr 2021 17:35

Last Modified:

14 Apr 2021 17:35

Publisher DOI:

10.3150/20-BEJ1256

BORIS DOI:

10.48350/154771

URI:

https://boris.unibe.ch/id/eprint/154771

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