Detecting abrupt changes in random fields

Free access article

Issue		ESAIM: PS Volume 6, 2002


Page(s)		189 - 209
DOI		10.1051/ps:2002011

ESAIM: P&S, November 2002, Vol. 6, pp. 189-209
DOI: 10.1051/ps:2002011

Detecting abrupt changes in random fields

Antoine Chambaz^{1, 2}

¹ UMR C 8628 du CNRS, Équipe de Probabilités, Statistique et Modélisation, Université Paris-Sud, France; Antoine.Chambaz@math.u-psud.fr.
² FTR&D, 38 rue du Général Leclerc, 92130 Issy-les-Moulineaux, France.

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 $\phi$ -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.

Mathematics Subject Classification. 60E15, 62C99, 62F12, 62G20, 62M40

Key words: Detection of change-points, M-estimation, penalized M-estimation, concentration inequalities, maximal inequalities, mixing.

© EDP Sciences, SMAI 2002

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