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.
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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 No 8.1.18.2018. On behalf of all authors, the corresponding author states that there is no conflict of interest.
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Chernoyarov, O.V., Kutoyants, Y.A. Poisson source localization on the plane: the smooth case. Metrika 83, 411–435 (2020). https://doi.org/10.1007/s00184-019-00738-1
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DOI: https://doi.org/10.1007/s00184-019-00738-1