Nonparametric statistical inference for compound models

This paper deals with the statistical inference in compound models, which are defined as a sum of i.i.d. random variables ξ1+⋯+ξN, where the number of summands, N, is a random variable independent of ξ1,ξ2,… Using the novel technique based on the superposition of the Mellin and Laplace transforms, we construct a nonparametric estimator for the distribution of N, assuming that the distribution of ξ is known explicitly. Unlike most papers on this topic, we consider the general setting, where the distribution of N is not necessarily of Poisson type.