Comptes Rendus
no. 7-8
Statistics
Change-point detection for continuous processes with high-frequency sampling
[Détection de rupture pour des processus continus avec un échantillonnage à haute fréquence]

Présenté par : Philippe G. Ciarlet

Guangming Wang1 ; Samir Ben Hariz2 ; Jonathan J. Wylie3 ; Qiang Zhang3
1 School of Mathematics and Statistics, Wuhan University, Hubei, 430072, People's Republic of China
2 Laboratoire de statistique et processus, département de mathématiques, université du Maine, avenue Olivier-Messiaen, 72085 Le Mans cedex 9, France
3 Department of Mathematics, City University of Hong Kong, 83, Tat Chee Avenue, Kowloon, Hong Kong
Comptes Rendus. Mathématique, Volume 346 (2008) no. 7-8, pp. 467-470.

Nous considérons la détection de saut dans un processus en temps continu sur un intervalle de temps fini et fixé. On cherche à localiser dans le temps la position de rupture via des observations discrètes. Nous étudions l'effet de croissance de la fréquence d'échantillonnage sur la précision de l'estimation. Nous montrons que la procédure classique avec les estimateurs à sommes cumulatives échoue et nous proposons une alternative basée sur une localisation de l'information. Nous prouvons que le nouvel estimateur converge avec une vitesse exponentielle.

We consider the detection of a jump in a continuous process over a fixed time interval. We aim to locate the jump position via discrete observations and consider how increasing the frequency of the observations affects the accuracy of the detection process. We show that the classical cumulative-sum estimator fails, and propose a new estimator based on local information that we prove converges exponentially fast.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2008.02.005
Guangming Wang 1 ; Samir Ben Hariz 2 ; Jonathan J. Wylie 3 ; Qiang Zhang 3

1 School of Mathematics and Statistics, Wuhan University, Hubei, 430072, People's Republic of China
2 Laboratoire de statistique et processus, département de mathématiques, université du Maine, avenue Olivier-Messiaen, 72085 Le Mans cedex 9, France
3 Department of Mathematics, City University of Hong Kong, 83, Tat Chee Avenue, Kowloon, Hong Kong 
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     title = {Change-point detection for continuous processes with high-frequency sampling},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {467--470},
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     doi = {10.1016/j.crma.2008.02.005},
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Guangming Wang; Samir Ben Hariz; Jonathan J. Wylie; Qiang Zhang. Change-point detection for continuous processes with high-frequency sampling. Comptes Rendus. Mathématique, Volume 346 (2008) no. 7-8, pp. 467-470. doi : 10.1016/j.crma.2008.02.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.02.005/

[1] M. Basseville; I.V. Nikiforov Detection of Abrupt Changes: Theory and Application, Prentice-Hall, Englewood Cliffs, NJ, 1993

[2] S. Ben Hariz, G.M. Wang, J.J. Wylie, Q. Zhang, Jump detection for discretely observed continuous processes, Preprint, 2007

[3] S. Ben Hariz; J.J. Wylie; Q. Zhang Optimal rate of convergence for nonparametric change-point estimators for non-stationary sequences, Ann. Statist., Volume 35 (2007), pp. 1802-1826

[4] E. Carlstein Nonparametric change-point estimation, Ann. Statist., Volume 16 (1988), pp. 188-197

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

[6] I.V. Nikiforov A generalized change detection problem, IEEE Trans. Inform. Theory, Volume 41 (1995) no. 1, pp. 171-187

[7] I.V. Nikiforov Two strategies in the problem of change detection and isolation, IEEE Trans. Inform. Theory, Volume 43 (1997) no. 2, pp. 770-776

[8] Y. Wang Jump and sharp cusp detection by wavelets, Biometrika, Volume 82 (1995) no. 2, pp. 385-397

[9] H. Wong; W. Ip; Y. Li Detection of jumps by wavelets in a heteroscedastic autoregressive model, Statist. Probab. Lett., Volume 52 (2001) no. 4, pp. 365-372

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