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Non-Uniform Bounds in the Poisson Approximation With Applications to Informational Distances I

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We explore asymptotically optimal bounds for deviations of Bernoulli convolutions from the Poisson limit in terms of the Shannon relative entropy and the Pearson $\chi ^{2}$ -distance. The results are… Click to show full abstract

We explore asymptotically optimal bounds for deviations of Bernoulli convolutions from the Poisson limit in terms of the Shannon relative entropy and the Pearson $\chi ^{2}$ -distance. The results are based on proper non-uniform estimates for densities. This part deals with the so-called non-degenerate case.

Keywords: approximation applications; poisson approximation; uniform bounds; applications informational; non uniform; bounds poisson

Journal Title: IEEE Transactions on Information Theory
Year Published: 2019

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