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Comptes Rendus Mathématique
Volume 341, n° 12
pages 765-768 (décembre 2005)
Doi : 10.1016/j.crma.2005.10.003
Received : 31 December 2004 ;  accepted : 26 September 2005
Convergence rates for estimating a change-point with long-range dependent sequences
Vitesses de convergence pour lʼestimation de rupture pour des suites fortements dépendantes
 

Samir Ben Hariz a , Jonathan J. Wylie b
a Laboratoire de statistique et processus, département de mathématiques, université du Maine, avenue Olivier-Messiaen, 72085 Le Mans cedex 9, France 
b Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong 

Abstract

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   convergence rate typical of the independent case is also achieved for short-memory and long-memory sequences. To cite this article: S. Ben Hariz, J.J. Wylie, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

The full text of this article is available in PDF format.
Résumé

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  , typique pour des suites indépendantes, est aussi obtenu pour des suites de courte ou de longue mémoire. Pour citer cet article : S. Ben Hariz, J.J. Wylie, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

The full text of this article is available in PDF format.
  The work described in this Note was fully supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CityU 1220/02P).


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