Poisson source localization on the plane: the smooth case O. V. Chernoyarov, Yu. A. Kutoyants
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ArticleContent type: Текст Media type: электронный Subject(s): неоднородный пуассоновский процесс | оценка максимального правдоподобия | байесовские оценки | локализация источниковGenre/Form: статьи в журналах Online resources: Click here to access online
In:
Metrika Vol. 83, № 4. P. 411-435Abstract: 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.
Библиогр.: c. 435
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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