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Estimation of the position and time of emission of a source

Author

Listed:
  • O. V. Chernoyarov

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

  • S. Dachian

    (University of Lille
    Tomsk State University)

  • C. Farinetto

    (Le Mans University)

  • Yu. A. Kutoyants

    (National Research University “MPEI”
    Tomsk State University)

Abstract

We consider the problem of the estimation of the position on the plane and of the moment of beginning of emission of a source by observations from K detectors on the plane. We propose the conditions of regularity and identifiability, which allow us to use two general theorems by Ibragimov and Khasminskii and to describe the asymptotic behavior of the maximum likelihood and Bayes estimators. Then we propose the construction of a linear estimator of unknown parameters and study its properties in slightly more general situation. Special attention is payed to condition of identifiability.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sistpr:v:25:y:2022:i:1:d:10.1007_s11203-021-09260-6
    DOI: 10.1007/s11203-021-09260-6
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    References listed on IDEAS

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    1. 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.
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