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Detecting abrupt changes in random fields

Published online by Cambridge University Press:  15 November 2002

Antoine Chambaz
Antoine Chambaz*
Affiliation:
UMR C 8628 du CNRS, Équipe de Probabilités, Statistique et Modélisation, Université Paris-Sud, France; Antoine.Chambaz@math.u-psud.fr. FTR&D, 38 rue du Général Leclerc, 92130 Issy-les-Moulineaux, France.
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Abstract

This paper is devoted to the study of some asymptotic properties of a M-estimator in a framework of detection of abrupt changes in random field's distribution. This class of problems includes e.g. recovery of sets. It involves various techniques, including M-estimation method, concentration inequalities, maximal inequalities for dependent random variables and ϕ-mixing. Penalization of the criterion function when the size of the true model is unknown is performed. All the results apply under mild, discussed assumptions. Simple examples are provided.

Keywords

Detection of change-pointsM-estimationpenalized M-estimationconcentration inequalitiesmaximal inequalitiesmixing.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 6: New directions in Time Series Analysis (Guest Editor: Philippe Soulier)New directions in Time Series Analysis (Guest Editor: Philippe Soulier) , 2002 , pp. 189 - 209
Copyright
© EDP Sciences, SMAI, 2002

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