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Poisson source localization on the plane: the smooth case

Author

Listed:
  • O. V. Chernoyarov

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

  • Yu. A. Kutoyants

    (Le Mans University
    Tomsk State University)

Abstract

We consider the problem of localization of a Poisson source using observations of inhomogeneous Poisson processes. We assume that k detectors are distributed on the plane and each detector generates observations of the Poisson processes, whose intensity functions depend on the position of the source. We study asymptotic properties of the maximum likelihood and Bayesian estimators of the source position on the plane assuming that the amplitude of the intensity functions are large. We show that under regularity conditions these estimators are consistent, asymptotically normal and asymptotically efficient in the minimax mean-square sense. Then we propose some simple consistent estimators and these estimators are further used to construct asymptotically efficient One-step MLE-process.

Suggested Citation

  • O. V. Chernoyarov & Yu. A. Kutoyants, 2020. "Poisson source localization on the plane: the smooth case," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(4), pages 411-435, May.
    • Handle: RePEc:spr:metrik:v:83:y:2020:i:4:d:10.1007_s00184-019-00738-1
    DOI: 10.1007/s00184-019-00738-1
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    References listed on IDEAS

    as
    1. Kutoyants, Yu.A., 2017. "On the multi-step MLE-process for ergodic diffusion," Stochastic Processes and their Applications, Elsevier, vol. 127(7), pages 2243-2261.
    2. S. Dachian, 2003. "Estimation of Cusp Location by Poisson Observations," Statistical Inference for Stochastic Processes, Springer, vol. 6(1), pages 1-14, January.
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    Cited by:

    1. Yury A. Kutoyants, 2021. "On localization of source by hidden Gaussian processes with small noise," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(4), pages 671-702, August.
    2. Arij Amiri & Sergueï Dachian, 2021. "On smooth change-point location estimation for Poisson Processes," Statistical Inference for Stochastic Processes, Springer, vol. 24(3), pages 499-524, October.
    3. O. V. Chernoyarov & S. Dachian & C. Farinetto & Yu. A. Kutoyants, 2022. "Estimation of the position and time of emission of a source," Statistical Inference for Stochastic Processes, Springer, vol. 25(1), pages 61-82, April.

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