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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

Abstract

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.

Citation

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

Information

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

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

Subjects:
Primary: 62L10
Secondary: 62N10

Rights: Copyright © 1997 Institute of Mathematical Statistics

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Vol.25 • No. 5 • October 1997
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