The Annals of Statistics

Optimality of the CUSUM procedure in continuous time

George V. Moustakides

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Abstract

The optimality of CUSUM under a Lorden-type criterion setting is considered. We demonstrate the optimality of the CUSUM test for Itô processes, in a sense similar to Lorden's, but with a criterion that replaces expected delays by the corresponding Kullback-Leibler divergence.

Article information

Source
Ann. Statist., Volume 32, Number 1 (2004), 302-315.

Dates
First available in Project Euclid: 12 March 2004

Permanent link to this document
https://projecteuclid.org/euclid.aos/1079120138

Digital Object Identifier
doi:10.1214/aos/1079120138

Mathematical Reviews number (MathSciNet)
MR2051009

Zentralblatt MATH identifier
1105.62368

Subjects
Primary: 62L10: Sequential analysis
Secondary: 62L15: Optimal stopping [See also 60G40, 91A60] 62C10: Bayesian problems; characterization of Bayes procedures

Keywords
CUSUM change point disorder problem sequential detection Kullback-Leibler divergence

Citation

Moustakides, George V. Optimality of the CUSUM procedure in continuous time. Ann. Statist. 32 (2004), no. 1, 302--315. doi:10.1214/aos/1079120138. https://projecteuclid.org/euclid.aos/1079120138


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