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December 1999 Detecting a change in regression: first-order optimality
Abba M. Krieger, Moshe Pollak, Benjamin Yakir
Ann. Statist. 27(6): 1896-1913 (December 1999). DOI: 10.1214/aos/1017939243


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.


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Abba M. Krieger. Moshe Pollak. Benjamin Yakir. "Detecting a change in regression: first-order optimality." Ann. Statist. 27 (6) 1896 - 1913, December 1999.


Published: December 1999
First available in Project Euclid: 4 April 2002

zbMATH: 0963.62077
MathSciNet: MR1765621
Digital Object Identifier: 10.1214/aos/1017939243

Primary: 62L10, 62N10

Rights: Copyright © 1999 Institute of Mathematical Statistics


Vol.27 • No. 6 • December 1999
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