Decompounding discrete distributions
A nonparametric Bayesian approach
Shota Gugushvili (Wageningen University & Research)
Ester Mariucci (University of Potsdam)
F.H. Van Der Meulen (TU Delft - Statistics)
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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 Markov chain Monte Carlo 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 plug-in 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→∞, it contracts around the “true,” data-generating parameters at rate 1/√n, up to a n factor.
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