Non-Uniform Bounds in the Poisson Approximation with Applications to Informational Distances. II

S. G. Bobkov; G. P. Chistyakov; F. Götze

Non-Uniform Bounds in the Poisson Approximation with Applications to Informational Distances. II

Probability 2019-08-15 v2

Authors: S. G. Bobkov , G. P. Chistyakov , F. Götze

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 R\'enyi/Tsallis relative distances (including Pearson's $\chi^2$ ). This part generalizes the results obtained in Part I and removes any constraints on the parameters of the Bernoulli distributions.

Keywords

poisson approximation non-uniform bounds shannon relative entropy renyi distance tsallis distance independent bernoulli variables

Cite

@article{arxiv.1906.09156,
  title  = {Non-Uniform Bounds in the Poisson Approximation with Applications to Informational Distances. II},
  author = {S. G. Bobkov and G. P. Chistyakov and F. Götze},
  journal= {arXiv preprint arXiv:1906.09156},
  year   = {2019}
}

Comments

This version uses our methods to treat R\'enyi/Tsallis relative distances as well. Furthermore, it discusses relations and overlaps with additional results for the non-degenerated cases in the literature we had not been aware of

Non-Uniform Bounds in the Poisson Approximation with Applications to Informational Distances. II

Abstract

Keywords

Cite

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