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Poisson source localization on the plane: cusp case

  • O. V. Chernoyarov
  • S. Dachian
  • Yu. A. KutoyantsEmail author
Article

Abstract

This work is devoted to the problem of estimation of the localization of Poisson source. The observations are inhomogeneous Poisson processes registered by more than three detectors on the plane. We study the behavior of the Bayes estimators in the asymptotic of large intensities. It is supposed that the intensity functions of the signals arriving in the detectors have cusp-type singularity. We show the consistency, limit distributions, the convergence of moments and asymptotic efficiency of these estimators.

Keywords

Inhomogeneous Poisson process Poisson source Sensors Bayes estimators Cusp-type singularity 

Notes

Acknowledgements

This work was done under partial financial support of the Grant of RSF Number 14-49-00079 and supported by the Tomsk State University Academic D.I. Mendeleev Fund Program under Grant Number 8.1.18.2018. Serguei Dachian acknowledges support from the Labex CEMPI (ANR-11-LABX-0007-01).

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Copyright information

© The Institute of Statistical Mathematics, Tokyo 2019

Authors and Affiliations

  • O. V. Chernoyarov
    • 1
    • 2
    • 3
  • S. Dachian
    • 3
    • 4
  • Yu. A. Kutoyants
    • 3
    • 5
    Email author
  1. 1.Department of Electronics and NanoelectronicsNational Research University “MPEI”MoscowRussia
  2. 2.Department of Higher Mathematics and System AnalysisMaikop State Technological UniversityMaikopRussia
  3. 3.International Laboratory of Statistics of Stochastic Processes and Quantitative FinanceNational Research Tomsk State UniversityTomskRussia
  4. 4.CNRS, UMR 8524 – Laboratoire Paul PainlevéUniversity of LilleLilleFrance
  5. 5.Laboratoire Manceau des MathematiquesLe Mans UniversityLe MansFrance

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