Decompounding discrete distributions: A nonparametric Bayesian approach
Abstract
Suppose that a compound Poisson process is observed discretely in time and assume that its jump distribution is supported on the set of natural numbers. In this paper we propose a nonparametric Bayesian approach to estimate the intensity of the underlying Poisson process and the distribution of the jumps. We provide a MCMC scheme for obtaining samples from the posterior. We apply our method on both simulated and real data examples, and compare its performance with the frequentist plugin estimator proposed by Buchmann and Grübel. On a theoretical side, we study the posterior from the frequentist point of view and prove that as the sample size $n\rightarrow\infty$, it contracts around the `true', datagenerating parameters at rate $1/\sqrt{n}$, up to a $\log n$ factor.
 Publication:

arXiv eprints
 Pub Date:
 March 2019
 arXiv:
 arXiv:1903.11142
 Bibcode:
 2019arXiv190311142G
 Keywords:

 Mathematics  Statistics Theory;
 62G20 (Primary);
 62M30 (Secondary)
 EPrint:
 27 pages, 7 figures