Statistics
Change-point detection for continuous processes with high-frequency sampling
Comptes Rendus. Mathématique, Volume 346 (2008) no. 7-8, pp. 467-470.

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.

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.

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DOI: 10.1016/j.crma.2008.02.005
Wang, Guangming 1; Ben Hariz, Samir 2; Wylie, Jonathan J. 3; Zhang, Qiang 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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Wang, Guangming; Ben Hariz, Samir; Wylie, Jonathan J.; Zhang, Qiang. 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. http://www.numdam.org/articles/10.1016/j.crma.2008.02.005/

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