Detecting abrupt changes in random fields
ESAIM: Probability and Statistics, Tome 6 (2002), pp. 189-209.

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.

DOI : https://doi.org/10.1051/ps:2002011
Classification : 60E15,  62C99,  62F12,  62G20,  62M40
Mots clés : detection of change-points, $M$-estimation, penalized $M$-estimation, concentration inequalities, maximal inequalities, mixing
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author = {Chambaz, Antoine},
title = {Detecting abrupt changes in random fields},
journal = {ESAIM: Probability and Statistics},
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doi = {10.1051/ps:2002011},
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language = {en},
url = {http://www.numdam.org/articles/10.1051/ps:2002011/}
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Chambaz, Antoine. Detecting abrupt changes in random fields. ESAIM: Probability and Statistics, Tome 6 (2002), pp. 189-209. doi : 10.1051/ps:2002011. http://www.numdam.org/articles/10.1051/ps:2002011/

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