Detecting abrupt changes in random fields

Antoine Chambaz (1)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5

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.

Domaines: Statistiques [math.ST]

Antoine Chambaz. Detecting abrupt changes in random fields. ESAIM: Probability and Statistics, 2002, 6, pp.189-209. ⟨hal-00143663⟩