The Annals of Statistics

On the average run length to false alarm in surveillance problems which possess an invariance structure

Benjamin Yakir

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Abstract

Surveillance can be based, in some change-point detection problems, on a sequence of invariant statistics. Gordon and Pollak prove that, under certain conditions, the average run length (ARL) to false alarm of invariance- based Shiryayev–Roberts detection schemes is asymptotically the same as that of the dual classical scheme that is based on the original sequence of observations. In this paper we give alternative conditions under which the two ARLs coincide and demonstrate that these conditions are satisfied in cases where Gordon and Pollak’s conditions are difficult to check.

Article information

Source
Ann. Statist. Volume 26, Number 3 (1998), 1198-1214.

Dates
First available in Project Euclid: 21 June 2002

Permanent link to this document
http://projecteuclid.org/euclid.aos/1024691095

Digital Object Identifier
doi:10.1214/aos/1024691095

Mathematical Reviews number (MathSciNet)
MR1635389

Zentralblatt MATH identifier
0932.62090

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

Keywords
Quality control control charts change-point detection invariant statistics

Citation

Yakir, Benjamin. On the average run length to false alarm in surveillance problems which possess an invariance structure. Ann. Statist. 26 (1998), no. 3, 1198--1214. doi:10.1214/aos/1024691095. http://projecteuclid.org/euclid.aos/1024691095.


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References

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