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.
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