A note on optimal detection of a change in distribution

Benjamin Yakir*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

29 Scopus citations

Abstract

Suppose X1, X2,..., Xv-1 are iid random variables with distribution F0, and Xv, Xv+1,... are are iid with distributed F1. The change point v is unknown. The problem is to raise an alarm as soon as possible after the distribution changes from F0 to F1 (detect the change), but to avoid false alarms. Pollak found a version of the Shiryayev-Roberts procedure to be asymptotically optimal for the problem of minimizing the average run length to detection over all stopping times which satisfy a given constraint on the rate of false alarms. Here we find that this procedure is strictly optimal for a slight reformulation of the problem he considered. Explicit formulas are developed for the calculation of the average run length (both before and after the change) for the optimal stopping time.

Original languageAmerican English
Pages (from-to)2117-2126
Number of pages10
JournalAnnals of Statistics
Volume25
Issue number5
DOIs
StatePublished - Oct 1997

Keywords

  • Bayes rule
  • Control charts
  • Minimax rule
  • Quality control

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