The Annals of Statistics

Average run length to false alarm for surveillance schemes designed with partially specified pre-change distribution

Louis Gordon and Moshe Pollak

Full-text: Open access

Abstract

Observations are taken independently and sequentially. Detection of a change in distribution is studied when the problem has an invariance structure. The prechange distribution is assumed to be a member of a specified family and is assumed known up to a nuisance parameter. We provide a general method of constructing surveillance schemes in the presence of a nuisance parameter and give sufficient conditions for approximating their average run lengths to false alarm. Applications include detecting a change in scale of i.i.d. gamma variates with unknown initial scale, detecting a change in location of i.i.d. normal variates with unknown initial mean, and a non-parametric scheme based on ranks for detecting a change to a stochastically larger distribution.

Article information

Source
Ann. Statist., Volume 25, Number 3 (1997), 1284-1310.

Dates
First available in Project Euclid: 20 November 2003

Permanent link to this document
https://projecteuclid.org/euclid.aos/1069362749

Digital Object Identifier
doi:10.1214/aos/1069362749

Mathematical Reviews number (MathSciNet)
MR1447752

Zentralblatt MATH identifier
0885.62092

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

Keywords
Cusum change-point disruption invariance

Citation

Gordon, Louis; Pollak, Moshe. Average run length to false alarm for surveillance schemes designed with partially specified pre-change distribution. Ann. Statist. 25 (1997), no. 3, 1284--1310. doi:10.1214/aos/1069362749. https://projecteuclid.org/euclid.aos/1069362749


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