Nonparametric estimation in random sum models


  • Hassan S. Bakouch Tanta University
  • Thomas A. Severini Northwestern University



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.


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How to Cite

Bakouch, H. S., & Severini, T. A. (2009). Nonparametric estimation in random sum models. Statistica, 69(1), 73–88.