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Misspecified change-point estimation problem for a Poisson process

Part of: Parametric inference Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Ali S. Dabye  and
Yury A. Kutoyants
Ali S. Dabye*
Affiliation:
Université de N'Djamena
Yury A. Kutoyants*
Affiliation:
Université du Maine
*
1Postal address: Faculté des Sciences Exactes et Appliquées, Université de N'Djamena, BP 1027, N'Djamena, Chad. Email: dabye@tit.td
2Postal address: Laboratoire de Statistique et Processus, Université du Maine, 72085 Le Mans, Cedex 9, France. Email: kutoyants@univ-lemans.fr
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Abstract

Consider an inhomogeneous Poisson process X on [0, T] whose unknown intensity function ‘switches' from a lower function g∗ to an upper function h∗ at some unknown point θ∗. What is known are continuous bounding functions g and h such that g∗(t) ≤ g(t) ≤ h(t) ≤ h∗(t) for 0 ≤ t ≤ T. It is shown that on the basis of n observations of the process X the maximum likelihood estimate of θ∗ is consistent for n →∞, and also that converges in law and in pth moment to limits described in terms of the unknown functions g∗ and h∗.

Keywords

Inhomogeneous Poisson processchange-type problemparameter estimationmisspecified modelconsistencylimit distribution

MSC classification

Primary: 62F12: Asymptotic properties of estimators
Secondary: 60G55: Point processes
Type
Estimation problems
Information
Journal of Applied Probability , Volume 38 , Issue A: Probability, Statistics and Seismology , 2001 , pp. 122 - 130
Copyright
Copyright © Applied Probability Trust 2001 

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References

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