Nonuniform bounds in the Poisson approximation with applications to informational distances. II

Sergey G. Bobkov; Gennadiy P. Chistyakov; Friedrich Götze

doi:10.1007/s10986-019-09468-3

Nonuniform bounds in the Poisson approximation with applications to informational distances. II

Sergey G. Bobkov, Gennadiy P. Chistyakov, Friedrich Götze

School of Mathematics

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1 Scopus citations

Abstract

We explore asymptotically optimal bounds for deviations of distributions of independent Bernoulli random variables from the Poisson limit in terms of the Shannon relative entropy and Rényi/relative Tsallis distances (including Pearson’s _2). This part generalizes the results obtained in Part I and removes any constraints on the parameters of the Bernoulli distributions.

Original language	English (US)
Pages (from-to)	469-497
Number of pages	29
Journal	Lithuanian Mathematical Journal
Volume	59
Issue number	4
DOIs	https://doi.org/10.1007/s10986-019-09468-3
State	Published - Oct 1 2019

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Publisher Copyright:
© 2019, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords

Poisson approximation
relative entropy
χ-divergence

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10.1007/s10986-019-09468-3

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AU - Chistyakov, Gennadiy P.

AU - Götze, Friedrich

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N2 - We explore asymptotically optimal bounds for deviations of distributions of independent Bernoulli random variables from the Poisson limit in terms of the Shannon relative entropy and Rényi/relative Tsallis distances (including Pearson’s _2). This part generalizes the results obtained in Part I and removes any constraints on the parameters of the Bernoulli distributions.

AB - We explore asymptotically optimal bounds for deviations of distributions of independent Bernoulli random variables from the Poisson limit in terms of the Shannon relative entropy and Rényi/relative Tsallis distances (including Pearson’s _2). This part generalizes the results obtained in Part I and removes any constraints on the parameters of the Bernoulli distributions.

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KW - relative entropy

KW - χ-divergence

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JF - Lithuanian Mathematical Journal

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ER -

Nonuniform bounds in the Poisson approximation with applications to informational distances. II

Abstract

Bibliographical note

Keywords

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