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October 1997 A note on optimal detection of a change in distribution
Benjamin Yakir
Ann. Statist. 25(5): 2117-2126 (October 1997). DOI: 10.1214/aos/1069362390


Suppose $X_1, X_2, \dots, X_{\nu - 1}$ are iid random variables with distribution $F_0$, and $X_{\nu}, X_{\nu + 1}, \dots$ are are iid with distributed $F_1$. The change point $\nu$ is unknown. The problem is to raise an alarm as soon as possible after the distribution changes from $F_0$ to $F_1$ (detect the change), but to avoid false alarms.

Pollak found a version of the Shiryayev-Roberts procedure to be asymptotically optimal for the problem of minimizing the average run length to detection over all stopping times which satisfy a given constraint on the rate of false alarms. Here we find that this procedure is strictly optimal for a slight reformulation of the problem he considered.

Explicit formulas are developed for the calculation of the average run length (both before and after the change) for the optimal stopping time.


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Benjamin Yakir. "A note on optimal detection of a change in distribution." Ann. Statist. 25 (5) 2117 - 2126, October 1997.


Published: October 1997
First available in Project Euclid: 20 November 2003

zbMATH: 0942.62088
MathSciNet: MR1474086
Digital Object Identifier: 10.1214/aos/1069362390

Primary: 62L10
Secondary: 62N10

Keywords: Bayes rule , control charts , minimax rule , quality control

Rights: Copyright © 1997 Institute of Mathematical Statistics


Vol.25 • No. 5 • October 1997
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