Multivariate Poisson-binomial approximation using Stein‘s method

Abstract

The paper is concerned with the accuracy in total variation of the approximation of the distribution of a sum of independent Bernoulli distributed random d–vectors by the product distribution with Poisson marginals which has the same mean. The best results, obtained using generating function methods, are those of Roos (1998, 1999). Stein's method has so far yielded somewhat weaker bounds. We demonstrate why a direct approach using Stein's method cannot emulate Roos's results, but give some less direct arguments to show that it is possible, using Stein's method, to get very close.