Detecting a change in regression: First-order optimality

Benjamin Yakir*, Abba M. Krieger, Moshe Pollak

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

28 Scopus citations


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.

Original languageAmerican English
Pages (from-to)1896-1913
Number of pages18
JournalAnnals of Statistics
Issue number6
StatePublished - Dec 1999


  • Change point detection
  • Information bound
  • Regression
  • Stopping rules


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