On Parameter Estimation by Aggregated Poisson Observations

We consider the problem of parameter estimation by the observations of inhomogeneous Poisson processes. The intensity function of the process is supposed to be a smooth function with respect to the unknown parameter. We propose a Chi-square statistic on the base of agregated observations and we def...

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Main Authors:	Elhadji Ousseynouu Accrachi, Cherif Ahmat Tidiane Aidara, Ali S. Dabye
Format:	Article
Language:	English
Published:	Republic of Armenia National Academy of Sciences 2019-04-01
Series:	Armenian Journal of Mathematics
Subjects:	Parameter estimation minimum chi-squared estimator agregated Poisson observations intensity function consistency asymptotic normality
Online Access:	http://www.armjmath.sci.am/index.php/ajm/article/view/257

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spelling	doaj-b121af4c7cee452392e5aa5eb1079f642020-11-25T00:02:24ZengRepublic of Armenia National Academy of SciencesArmenian Journal of Mathematics1829-11632019-04-01115On Parameter Estimation by Aggregated Poisson ObservationsElhadji Ousseynouu AccrachiCherif Ahmat Tidiane AidaraAli S. Dabye We consider the problem of parameter estimation by the observations of inhomogeneous Poisson processes. The intensity function of the process is supposed to be a smooth function with respect to the unknown parameter. We propose a Chi-square statistic on the base of agregated observations and we define a Minimum Chi-square Estimator with the help of this statistics. We show this that estimator is consistent and asymptotically normal. We discuss possible generalizations of the obtained results. http://www.armjmath.sci.am/index.php/ajm/article/view/257Parameter estimationminimum chi-squared estimatoragregated Poisson observationsintensity functionconsistencyasymptotic normality
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Elhadji Ousseynouu Accrachi Cherif Ahmat Tidiane Aidara Ali S. Dabye
spellingShingle	Elhadji Ousseynouu Accrachi Cherif Ahmat Tidiane Aidara Ali S. Dabye On Parameter Estimation by Aggregated Poisson Observations Armenian Journal of Mathematics Parameter estimation minimum chi-squared estimator agregated Poisson observations intensity function consistency asymptotic normality
author_facet	Elhadji Ousseynouu Accrachi Cherif Ahmat Tidiane Aidara Ali S. Dabye
author_sort	Elhadji Ousseynouu Accrachi
title	On Parameter Estimation by Aggregated Poisson Observations
title_short	On Parameter Estimation by Aggregated Poisson Observations
title_full	On Parameter Estimation by Aggregated Poisson Observations
title_fullStr	On Parameter Estimation by Aggregated Poisson Observations
title_full_unstemmed	On Parameter Estimation by Aggregated Poisson Observations
title_sort	on parameter estimation by aggregated poisson observations
publisher	Republic of Armenia National Academy of Sciences
series	Armenian Journal of Mathematics
issn	1829-1163
publishDate	2019-04-01
description	We consider the problem of parameter estimation by the observations of inhomogeneous Poisson processes. The intensity function of the process is supposed to be a smooth function with respect to the unknown parameter. We propose a Chi-square statistic on the base of agregated observations and we define a Minimum Chi-square Estimator with the help of this statistics. We show this that estimator is consistent and asymptotically normal. We discuss possible generalizations of the obtained results.
topic	Parameter estimation minimum chi-squared estimator agregated Poisson observations intensity function consistency asymptotic normality
url	http://www.armjmath.sci.am/index.php/ajm/article/view/257
work_keys_str_mv	AT elhadjiousseynouuaccrachi onparameterestimationbyaggregatedpoissonobservations AT cherifahmattidianeaidara onparameterestimationbyaggregatedpoissonobservations AT alisdabye onparameterestimationbyaggregatedpoissonobservations
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On Parameter Estimation by Aggregated Poisson Observations

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