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June 1997 Average run length to false alarm for surveillance schemes designed with partially specified pre-change distribution
Louis Gordon, Moshe Pollak
Ann. Statist. 25(3): 1284-1310 (June 1997). DOI: 10.1214/aos/1069362749

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.

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Louis Gordon. Moshe Pollak. "Average run length to false alarm for surveillance schemes designed with partially specified pre-change distribution." Ann. Statist. 25 (3) 1284 - 1310, June 1997. https://doi.org/10.1214/aos/1069362749

Information

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

zbMATH: 0885.62092
MathSciNet: MR1447752
Digital Object Identifier: 10.1214/aos/1069362749

Subjects:
Primary: 62L10
Secondary: 62N10

Rights: Copyright © 1997 Institute of Mathematical Statistics

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Vol.25 • No. 3 • June 1997
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