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

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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.

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Acknowledgements

The authors are grateful to Associate Editor and Reviewer for useful comments. This research was financially supported by the Ministry of Education and Science of the Russian Federation (research project No. FSWF-2020-0022) and by RFBR and CNRS (research project No. 20-51-15001).

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Authors and Affiliations

  1. National Research University “MPEI”, Moscow, Russia

    O. V. Chernoyarov & Y. A. Kutoyants

  2. Maikop State Technological University, Maikop, Russia

    O. V. Chernoyarov

  3. University Gaston Berger, Saint Louis, Senegal

    A. S. Dabye

  4. University of Thies, Thies, Senegal

    F. N. Diop

  5. Le Mans University, Le Mans, France

    Y. A. Kutoyants

  6. Tomsk State University, Tomsk, Russia

    O. V. Chernoyarov & Y. A. Kutoyants

Authors
  1. O. V. Chernoyarov
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  2. A. S. Dabye
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  3. F. N. Diop
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  4. Y. A. Kutoyants
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Correspondence to Y. A. Kutoyants.

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Chernoyarov, O.V., Dabye, A.S., Diop, F.N. et al. Non asymptotic expansions of the MME in the case of Poisson observations. Metrika 85, 927–950 (2022). https://doi.org/10.1007/s00184-021-00855-w

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  • DOI: https://doi.org/10.1007/s00184-021-00855-w

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