Annals of Statistics

Detecting a change in regression: first-order optimality

Abba M. Krieger, Moshe Pollak, and Benjamin Yakir

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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

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

First available in Project Euclid: 4 April 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62L10: Sequential analysis 62N10

Change point detection regression stopping rules information bound


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.

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