Decompounding discrete distributions: A non-parametric Bayesian approach

03/26/2019

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by   Shota Gugushvili, et al.

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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 non-parametric 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 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.