The Annals of Statistics

An Efficient Sequential Nonparametric Scheme for Detecting a Change of Distribution

Louis Gordon and Moshe Pollak

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist., Volume 22, Number 2 (1994), 763-804.

Dates
First available in Project Euclid: 11 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176325495

Digital Object Identifier
doi:10.1214/aos/1176325495

Mathematical Reviews number (MathSciNet)
MR1292540

Zentralblatt MATH identifier
0816.62066

JSTOR
links.jstor.org

Subjects
Primary: 62L10: Sequential analysis
Secondary: 62N10

Keywords
Cusum changepoint disruption

Citation

Gordon, Louis; Pollak, Moshe. An Efficient Sequential Nonparametric Scheme for Detecting a Change of Distribution. Ann. Statist. 22 (1994), no. 2, 763--804. doi:10.1214/aos/1176325495. https://projecteuclid.org/euclid.aos/1176325495


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