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Non asymptotic expansions of the MME in the case of Poisson observations

Author

Listed:
  • O. V. Chernoyarov

    (National Research University “MPEI”
    Maikop State Technological University
    Tomsk State University)

  • A. S. Dabye

    (University Gaston Berger)

  • F. N. Diop

    (University of Thies)

  • Y. A. Kutoyants

    (National Research University “MPEI”
    Le Mans University
    Tomsk State University)

Abstract

In this paper the problem of one dimensional parameter estimation is considered in the case where observations are coming from inhomogeneous Poisson processes. The method of moments estimation is studied and its stochastic expansion is obtained. This stochastic expansion is then used to obtain the expansion of the moments of the estimator and the expansion of the distribution function. The stochastic expansion, the expansion of the moments and the expansion of distribution function are non asymptotic in nature. Several examples are presented to illustrate the theoretical results.

Suggested Citation

  • O. V. Chernoyarov & A. S. Dabye & F. N. Diop & Y. A. Kutoyants, 2022. "Non asymptotic expansions of the MME in the case of Poisson observations," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(8), pages 927-950, November.
    • Handle: RePEc:spr:metrik:v:85:y:2022:i:8:d:10.1007_s00184-021-00855-w
    DOI: 10.1007/s00184-021-00855-w
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    References listed on IDEAS

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    1. Gutti Babu & Kesar Singh & Yaning Yang, 2003. "Edgeworth expansions for compound Poisson processes and the bootstrap," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(1), pages 83-94, March.
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