[Détection de rupture pour des processus continus avec un échantillonnage à haute fréquence]
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.
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@article{CRMATH_2008__346_7-8_467_0,
author = {Wang, Guangming and Ben Hariz, Samir and Wylie, Jonathan J. and Zhang, Qiang},
title = {Change-point detection for continuous processes with high-frequency sampling},
journal = {Comptes Rendus. Math\'ematique},
pages = {467--470},
publisher = {Elsevier},
volume = {346},
number = {7-8},
year = {2008},
doi = {10.1016/j.crma.2008.02.005},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2008.02.005/}
}
TY - JOUR AU - Wang, Guangming AU - Ben Hariz, Samir AU - Wylie, Jonathan J. AU - Zhang, Qiang TI - Change-point detection for continuous processes with high-frequency sampling JO - Comptes Rendus. Mathématique PY - 2008 SP - 467 EP - 470 VL - 346 IS - 7-8 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2008.02.005/ DO - 10.1016/j.crma.2008.02.005 LA - en ID - CRMATH_2008__346_7-8_467_0 ER -
%0 Journal Article %A Wang, Guangming %A Ben Hariz, Samir %A Wylie, Jonathan J. %A Zhang, Qiang %T Change-point detection for continuous processes with high-frequency sampling %J Comptes Rendus. Mathématique %D 2008 %P 467-470 %V 346 %N 7-8 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2008.02.005/ %R 10.1016/j.crma.2008.02.005 %G en %F CRMATH_2008__346_7-8_467_0
Wang, Guangming; Ben Hariz, Samir; Wylie, Jonathan J.; Zhang, Qiang. Change-point detection for continuous processes with high-frequency sampling. Comptes Rendus. Mathématique, Tome 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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