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Small noise asymptotics of the GLR test for off-line change detection in misspecified diffusion processes

Fabien Campillo 1 Yuri Kutoyants 2 François Le Gland 3
1 SYSDYS - Stochastic Dynamical Systems
CRISAM - Inria Sophia Antipolis - Méditerranée
3 ASPI - Applications of interacting particle systems to statistics
UR1 - Université de Rennes 1, Inria Rennes – Bretagne Atlantique , CNRS - Centre National de la Recherche Scientifique : UMR6074
Abstract : We consider the problem of the non-sequential detection of a change in the drift coefficient of a stochastic differential equation, when a misspecified model is used. We formulate the generalized likelihood ratio (GLR) test for this problem, and we study the behaviour of the associated error probabilities (false alarm and nodetection) in the small noise asymptotics. We obtain the following robustness result: even though a wrong model is used, the error probabilities go to zero with exponential rate, and the maximum likelihood estimator (MLE) of the change time is consistent, provided the change to be detected is larger (in some sense) than the misspecification error. We give also computable bounds for selecting the threshold of the test so as to achieve these exponential rates.
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https://hal.inria.fr/hal-00652116
Contributor : Fabien Campillo <>
Submitted on : Wednesday, December 14, 2011 - 11:00:28 PM
Last modification on : Wednesday, May 16, 2018 - 11:23:02 AM

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Fabien Campillo, Yuri Kutoyants, François Le Gland. Small noise asymptotics of the GLR test for off-line change detection in misspecified diffusion processes. Stochastics and Stochastics Reports, Informa UK (Taylor & Francis), 2000, 70 (1--2), pp.109--129. ⟨10.1080/17442500008834247⟩. ⟨hal-00652116⟩

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