Comptes Rendus
no. 12
Statistics
Convergence rates for estimating a change-point with long-range dependent sequences
[Vitesses de convergence pour l'estimation de rupture pour des suites fortements dépendantes]

Présenté par : Philippe G. Ciarlet

Samir Ben Hariz1 ; Jonathan J. Wylie2
1 Laboratoire de statistique et processus, département de mathématiques, université du Maine, avenue Olivier-Messiaen, 72085 Le Mans cedex 9, France
2 Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong
Comptes Rendus. Mathématique, Volume 341 (2005) no. 12, pp. 765-768.

Nous considérons une suite éventuellement fortement dépendante, avec un saut dans sa moyenne. Nous estimons le temps de rupture à partir des sommes partielles. La vitesse de convergence 1/n, typique pour des suites indépendantes, est aussi obtenu pour des suites de courte ou de longue mémoire.

We consider a (possibly) long-range dependent sequence with a shift in the mean. We estimate the location of the change-point using a cumulative sum estimator. The 1/n convergence rate typical of the independent case is also achieved for short-memory and long-memory sequences.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2005.10.003
Samir Ben Hariz 1 ; Jonathan J. Wylie 2

1 Laboratoire de statistique et processus, département de mathématiques, université du Maine, avenue Olivier-Messiaen, 72085 Le Mans cedex 9, France
2 Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong 
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Samir Ben Hariz; Jonathan J. Wylie. Convergence rates for estimating a change-point with long-range dependent sequences. Comptes Rendus. Mathématique, Volume 341 (2005) no. 12, pp. 765-768. doi : 10.1016/j.crma.2005.10.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.10.003/

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[2] M. Csörgő; L. Horváth Limit Theorems in Change-Point Analysis, Wiley, Chichester, 1997

[3] L. Dumbgen The asymptotic behavior of some nonparametric change-point estimators, Ann. Statist., Volume 19 (1991), pp. 1471-1495

[4] D. Ferger Exponential and polynomial tailbounds for change-point estimators, J. Statist. Plann. Inference, Volume 92 (2001), pp. 73-109

[5] L. Giraitis; R. Leipus; D. Surgailis The change-point problem for dependent observations, J. Statist. Plann. Inference, Volume 53 (1996), pp. 297-310

[6] L. Horváth; P. Kokoszka The effect of long-range dependence on change-point estimators, J. Statist. Plann. Inference, Volume 64 (1997), pp. 57-81

[7] P. Kokoszka; R. Leipus Change-point in the mean of dependent observations, Statist. Probab. Lett., Volume 40 (1998), pp. 385-393

[8] F. Moricz Moment inequalities and the strong laws of large numbers, Z. Wahrscheinlichkeitstheorie Verw. Gebiete, Volume 35 (1976) no. 4, pp. 299-314

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