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Estimation of linear functionals of Poisson processes

Author

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  • Kutoyants, Yu. A.
  • Liese, F.

Abstract

For i.i.d. Poisson point processes with intensity measure [Lambda] an estimator for [theta][infinity]([Lambda]) = [integral operator] [infinity] d[Lambda] is introduced. Consistency as well as rates for the convergence are established. An Edgeworth-type expansion for the distribution function is obtained. The estimator is asymptotically efficient in the sense of LAN-theory.

Suggested Citation

  • Kutoyants, Yu. A. & Liese, F., 1998. "Estimation of linear functionals of Poisson processes," Statistics & Probability Letters, Elsevier, vol. 40(1), pages 43-55, September.
    • Handle: RePEc:eee:stapro:v:40:y:1998:i:1:p:43-55
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    References listed on IDEAS

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    1. Ivanoff, Gail, 1982. "Central limit theorems for point processes," Stochastic Processes and their Applications, Elsevier, vol. 12(2), pages 171-186, March.
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    Cited by:

    1. Olivier Collier & Arnak S. Dalalyan, 2018. "Estimating linear functionals of a sparse family of Poisson means," Statistical Inference for Stochastic Processes, Springer, vol. 21(2), pages 331-344, July.
    2. Olivier Collier & Arnak Dalalyan, 2017. "Estimating linear functionals of a sparse family of Poisson means Price Discrimination," Working Papers 2017-19, Center for Research in Economics and Statistics.

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