On multiple change-point estimation for Poisson process

This work is devoted to the problem of change-point parameter estimation in the case of the presence of multiple changes in the intensity function of the Poisson process. It is supposed that the observations are independent inhomogeneous Poisson processes with the same intensity function and this in...

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Bibliographic Details
Published inCommunications in statistics. Theory and methods Vol. 47; no. 5; pp. 1215 - 1233
Main Authors Chernoyarov, O. V., Kutoyants, Yu. A., Top, A.
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 04.03.2018
Taylor & Francis Ltd
Subjects
Bayesian analysis
Bayesian estimator
change-point
Computer simulation
inhomogeneous Poisson process
likelihood ratio process
Mathematics
Maximum likelihood estimators
maximum-likelihood estimator
Parameter estimation
Poisson density functions
Statistics
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Summary:This work is devoted to the problem of change-point parameter estimation in the case of the presence of multiple changes in the intensity function of the Poisson process. It is supposed that the observations are independent inhomogeneous Poisson processes with the same intensity function and this intensity function has two jumps separated by a known quantity. The asymptotic behavior of the maximum-likelihood and Bayesian estimators are described. It is shown that these estimators are consistent, have different limit distributions, the moments converge and that the Bayesian estimators are asymptotically efficient. The numerical simulations illustrate the obtained results.
ISSN:0361-0926
1532-415X
DOI:10.1080/03610926.2017.1317810