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May 2021 Bounding distributional errors via density ratios
Lutz Dümbgen, Richard J. Samworth, Jon A. Wellner
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Bernoulli 27(2): 818-852 (May 2021). DOI: 10.3150/20-BEJ1256

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.

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Lutz Dümbgen. Richard J. Samworth. Jon A. Wellner. "Bounding distributional errors via density ratios." Bernoulli 27 (2) 818 - 852, May 2021. https://doi.org/10.3150/20-BEJ1256

Information

Received: 1 July 2019; Revised: 1 January 2020; Published: May 2021
First available in Project Euclid: 24 March 2021

Digital Object Identifier: 10.3150/20-BEJ1256

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

Rights: Copyright © 2021 ISI/BS

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Vol.27 • No. 2 • May 2021
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