Misspecified change-point estimation problem for a Poisson process

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 show...

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Bibliographic Details
Published in:Journal of applied probability 2001, Vol.38 (A), p.122-130
Main Authors: Dabye, Ali S., Kutoyants, Yury A.
Format: Article
Language:English
Subjects:
60G55
62F12
change-type problem
consistency
Consistent estimators
Estimation Problems
Estimators
Inhomogeneous Poisson process
limit distribution
Mathematical functions
Mathematical independent variables
Maximum likelihood estimation
Maximum likelihood estimators
misspecified model
parameter estimation
Poisson process
Random variables
Statistics
Stochastic processes
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Summary: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 ∗.
ISSN:0021-9002
1475-6072
DOI:10.1239/jap/1085496596