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

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/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.

This version uses our methods to treat Rényi/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