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September, 1990 Decision Theoretic Optimality of the Cusum Procedure
Y. Ritov
Ann. Statist. 18(3): 1464-1469 (September, 1990). DOI: 10.1214/aos/1176347761

Abstract

Suppose $X_1, X_2, \ldots$ are independent random variables such that for some unknown $\nu$, each of $X_1, \ldots, X_{\nu - 1}$ is distributed according to $F_0$, while $X_\nu, X_{\nu + 1}, \ldots$ are all distributed according to $F_1$. We prove a result of Moustakides that claims that the CUSUM procedures are optimal in the sense of Lorden. We do that by proving that the procedures are Bayes for some stochastic mechanism of generating $\nu$.

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Y. Ritov. "Decision Theoretic Optimality of the Cusum Procedure." Ann. Statist. 18 (3) 1464 - 1469, September, 1990. https://doi.org/10.1214/aos/1176347761

Information

Published: September, 1990
First available in Project Euclid: 12 April 2007

zbMATH: 0712.62073
MathSciNet: MR1062720
Digital Object Identifier: 10.1214/aos/1176347761

Subjects:
Primary: 62L10
Secondary: 62L15

Rights: Copyright © 1990 Institute of Mathematical Statistics

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Vol.18 • No. 3 • September, 1990
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