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June, 1994 An Efficient Sequential Nonparametric Scheme for Detecting a Change of Distribution
Louis Gordon, Moshe Pollak
Ann. Statist. 22(2): 763-804 (June, 1994). DOI: 10.1214/aos/1176325495


Suppose that a system in its standard state produces i.i.d. observations whose distribution is symmetric about zero. At an unknown time the system may leave its standard state, and the observations would subsequently be stochastically larger. Subject to a bound on the rate of false alarms, one wants to detect quickly such a departure from the standard state. We present a robust method of detection which is computationally feasible and remarkably efficient. The method is based on the sequential vectors of signs and ranks of the observations. The methodology is one of likelihood ratio; a sequence of likelihood ratios for these vectors is computed, and the Shiryayev-Roberts approach to changepoint detection is then applied to yield a class of statistics and associated stopping rules. Inequalities and asymptotic approximations for the operating characteristics of these rules are developed. These are found to be valid also for small average run lengths and early changepoints as well. The relative efficiency of these schemes (with respect to a normal parametric shift detection policy) is very high, making them a robust alternative to parametric methods.


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Louis Gordon. Moshe Pollak. "An Efficient Sequential Nonparametric Scheme for Detecting a Change of Distribution." Ann. Statist. 22 (2) 763 - 804, June, 1994.


Published: June, 1994
First available in Project Euclid: 11 April 2007

zbMATH: 0816.62066
MathSciNet: MR1292540
Digital Object Identifier: 10.1214/aos/1176325495

Primary: 62L10
Secondary: 62N10

Keywords: changepoint , CUSUM , disruption

Rights: Copyright © 1994 Institute of Mathematical Statistics


Vol.22 • No. 2 • June, 1994
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