New bounds for union-free families of sets.

Coppersmith, Don; Shearer, James B.

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Detecting abrupt changes in random fields

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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...