@article{Bakouch_Severini_2009, title={Nonparametric estimation in random sum models}, volume={69}, url={https://rivista-statistica.unibo.it/article/view/3549}, DOI={10.6092/issn.1973-2201/3549}, abstractNote={Let X1,X2,…,XN be independent, identically distributed, non-negative, integervalued random variables and let N be a non-negative, integer-valued random variable independent of X1,X2,…,XN . In this paper, we consider two nonparametric estimation problems for the random sum variable. The first is the estimation of the means of Xi and N based on the second-moment assumptions on distributions of Xi and N . The second is the nonparametric estimation of the distribution of Xi given a parametric model for the distribution of N . Some asymptotic properties of the proposed estimators are discussed.}, number={1}, journal={Statistica}, author={Bakouch, Hassan S. and Severini, Thomas A.}, year={2009}, month={Jan.}, pages={73–88} }