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December 1998 Quickest detection with exponential penalty for delay
H. Vincent Poor
Ann. Statist. 26(6): 2179-2205 (December 1998). DOI: 10.1214/aos/1024691466

Abstract

The problem of detecting a change in the probability distribution of a random sequence is considered. Stopping times are derived that optimize the tradeoff between detection delay and false alarms within two criteria. In both cases, the detection delay is penalized exponentially rather than linearly, as has been the case in previous formulations of this problem. The first of these two criteria is to minimize a worst-case measure of the exponential detection delay within a lower-bound constraint on the mean time between false alarms. Expressions for the performance of the optimal detection rule are also developed for this case. It is seen, for example, that the classical Page CUSUM test can be arbitrarily unfavorable relative to the optimal test under exponential delay penalty. The second criterion considered is a Bayesian one, in which the unknown change point is assumed to obey a geometric prior distribution. In this case, the optimal stopping time effects an optimal trade-off between the expected exponential detection delay and the probability of false alarm. Finally, generalizations of these results to problems in which the penalties for delay may be path dependent are also considered.

Citation

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H. Vincent Poor. "Quickest detection with exponential penalty for delay." Ann. Statist. 26 (6) 2179 - 2205, December 1998. https://doi.org/10.1214/aos/1024691466

Information

Published: December 1998
First available in Project Euclid: 21 June 2002

zbMATH: 0927.62077
MathSciNet: MR1700227
Digital Object Identifier: 10.1214/aos/1024691466

Subjects:
Primary: 62L10
Secondary: 60G40, 62L15, 94A13

Rights: Copyright © 1998 Institute of Mathematical Statistics

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Vol.26 • No. 6 • December 1998
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