The Annals of Statistics

Detecting a change in regression: first-order optimality

Abba M. Krieger, Moshe Pollak, and Benjamin Yakir

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Abstract

Observations are generated according to a regression with normal error as a function of time,when the process is in control. The process potentially changes at some unknown point oftime and then the ensuing observations are normal with the same mean function plus an arbitrary function under suitable regularity conditions. The problem is to obtain a stopping rule that is optimal in the sense that the rule minimizes the expected delay in detecting a change subject to a constraint on the average run length to a false alarm. A bound on the expected delay is first obtained. It is then shown that the cusum and Shiryayev–Roberts procedures achieve this bound to first order.

Article information

Source
Ann. Statist., Volume 27, Number 6 (1999), 1896-1913.

Dates
First available in Project Euclid: 4 April 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1017939243

Digital Object Identifier
doi:10.1214/aos/1017939243

Mathematical Reviews number (MathSciNet)
MR1765621

Zentralblatt MATH identifier
0963.62077

Subjects
Primary: 62L10: Sequential analysis 62N10

Keywords
Change point detection regression stopping rules information bound

Citation

Yakir, Benjamin; Krieger, Abba M.; Pollak, Moshe. Detecting a change in regression: first-order optimality. Ann. Statist. 27 (1999), no. 6, 1896--1913. doi:10.1214/aos/1017939243. https://projecteuclid.org/euclid.aos/1017939243


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