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Estimating linear functionals in Poisson mixture models

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  • Laurent Cavalier
  • Nicolas Hengartner

Abstract

This paper concerns the problem of estimating linear functionals of the mixing distribution from Poisson mixture observations. In particular, linear functionals for which a parametric rate of convergence cannot be achieved are studied. It appears that Gaussian functionals are rather easy to estimate. Estimation of the distribution functions is then considered by approximating this functional using Gaussian functionals. Finally, the case of smooth distribution functions is considered in order to deal with rather general linear functionals.

Suggested Citation

  • Laurent Cavalier & Nicolas Hengartner, 2009. "Estimating linear functionals in Poisson mixture models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(6), pages 713-728.
    • Handle: RePEc:taf:gnstxx:v:21:y:2009:i:6:p:713-728
    DOI: 10.1080/10485250902971716
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    References listed on IDEAS

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    1. Wang, Ji-Ping, 2007. "A linearization procedure and a VDM/ECM algorithm for penalized and constrained nonparametric maximum likelihood estimation for mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 2946-2957, March.
    2. Wang, Ji-Ping Z. & Lindsay, Bruce G., 2005. "A Penalized Nonparametric Maximum Likelihood Approach to Species Richness Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 942-959, September.
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