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

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 r...

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Bibliographic Details
Published in:Lithuanian mathematical journal 2019-10, Vol.59 (4), p.469-497
Main Authors: Bobkov, Sergey G., Chistyakov, Gennadiy P., Götze, Friedrich
Format: Article
Language:English
Subjects:
Actuarial Sciences
Mathematics
Mathematics and Statistics
Number Theory
Ordinary Differential Equations
Probability Theory and Stochastic Processes
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Summary: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.
ISSN:0363-1672
1573-8825
DOI:10.1007/s10986-019-09468-3