Yakir, Benjamin; Krieger, Abba M.; Pollak, Moshe Detecting a change in regression: First-order optimality. (English) Zbl 0963.62077 Ann. Stat. 27, No. 6, 1896-1913 (1999). Summary: 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 of time 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. Cited in 1 ReviewCited in 17 Documents MSC: 62L15 Optimal stopping in statistics 62P30 Applications of statistics in engineering and industry; control charts 62L10 Sequential statistical analysis Keywords:change point detection; information bound × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Lai, T. L. (1993). Information bounds and quick detection of parameter changes in stochastic systems. Technical report, Stanford Univ. [2] Lai, T. L. (1995). Sequential changepoint detection in quality control and dynamical systems. J. Roy. Statist. Soc. Ser. B 57 613-658. JSTOR: · Zbl 0832.62072 [3] Lorden, G. (1971). Procedures for reacting to a change in distribution. Ann. Math. Statist. 42 1897-1908. · Zbl 0255.62067 · doi:10.1214/aoms/1177693055 [4] Moustakides, G. V. (1986). Optimal stopping times for detecting changes in distributions. Ann. Statist. 14 1379-1387. · Zbl 0612.62116 · doi:10.1214/aos/1176350164 [5] Pollak, M. (1985). Optimal detection ofa change in distribution. Ann. Statist. 13 206-227. · Zbl 0573.62074 · doi:10.1214/aos/1176346587 [6] Pollak, M. and Siegmund, D. (1985). A diffusion process and its application to detecting a change in the drift of a Brownian motion. Biometrika 72 267-280. JSTOR: · Zbl 0571.60084 · doi:10.1093/biomet/72.2.267 [7] Ritov, Y. (1990). Decision theoretic optimality ofthe CUSUM procedure. Ann. Statist. 18 1464- 1469. · Zbl 0712.62073 · doi:10.1214/aos/1176347761 [8] Robbins, H. and Zhang, C.-H. (1993). A change point problem with some applications. Technical report, Rutgers Univ. [9] Yakir, B. (1996). A lower bound on the ARL to detection with a probability constraint on false alarm. Ann. Statist. 24 431-435. · Zbl 0853.62063 · doi:10.1214/aos/1033066219 [10] Yakir, B. (1997). A note on optimal detection ofa change in distribution. Ann. Statist. 25 21172126. · Zbl 0942.62088 · doi:10.1214/aos/1069362390 [11] Yao, Q. (1993). Asymptotically optimal detection ofa change in a linear model. Sequential Anal. 12 201-210. · Zbl 0793.62043 · doi:10.1080/07474949308836279 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.