This paper is devoted to the study of some asymptotic properties of a -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 -estimation method, concentration inequalities, maximal inequalities for dependent random variables and -mixing. Penalization of the criterion function when the size of the true model is unknown is performed. All the results apply under mild,...
This paper is devoted to the study of some asymptotic properties of a
-estimator in a framework of detection of abrupt changes in
random field's distribution. This class of problems includes
recovery of sets. It involves various
techniques, including -estimation method, concentration
inequalities, maximal inequalities for dependent random variables and
-mixing. Penalization of the criterion function when the size of the
true model is
unknown is performed. All the results apply under mild,...
This paper deals with order identification for Markov chains with Markov
regime (MCMR) in the context of finite alphabets. We define the joint order
of a MCMR process in terms of the number of states of the hidden Markov
chain and the memory of the conditional Markov chain. We study the
properties of penalized maximum likelihood estimators for the unknown order
of an observed MCMR process, relying on information theoretic
arguments. The novelty of our work relies in the joint estimation...
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