Poisson source localization on the plane: the smooth case
| Autor: | Yury A. Kutoyants, Oleg V. Chernoyarov |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
Plane (geometry) 05 social sciences Bayesian probability Mathematical analysis Estimator Minimax Poisson distribution 01 natural sciences локализация источников оценка максимального правдоподобия неоднородный пуассоновский процесс 010104 statistics & probability symbols.namesake Amplitude Position (vector) Simple (abstract algebra) 0502 economics and business symbols байесовские оценки 0101 mathematics Statistics Probability and Uncertainty 050205 econometrics Mathematics |
| Zdroj: | Metrika. 2020. Vol. 83, № 4. P. 411-435 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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