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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 aM-estimator in a framework of detection of abrupt changes inrandom field's distribution. This class of problems includes e.g.recovery of sets. It involves various techniques, including M-estimation method, concentrationinequalities, maximal inequalities for dependent random variables and ϕ-mixing. Penalization of the criterion function when the size of thetrue model is unknown is performed. All the results apply under mild, discussedassumptions. Simple examples are provided.

Keywords

Detection of change-pointsM-estimationpenalized M-estimationconcentration inequalitiesmaximal inequalitiesmixing.

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