Optimality properties of the shiryaev-roberts procedure

Moshe Pollak*, Alexander G. Tartakovsky

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

71 Scopus citations

Abstract

In 1961, for detecting a change in the drift of a Brownian motion, Shiryaev introduced what is now usually referred to as the Shiryaev-Roberts procedure. This procedure has a number of optimality and asymptotic optimality properties in various settings. Shiryaev (1961, 1963), and more recently Feinberg and Shiryaev (2006), established exact optimality properties in the context of monitoring a Brownian motion for a (known) change of drift. Their method of proof relies on techniques particular to Brownian motion that are not applicable in discrete time. Here we establish analogous results in a general discrete time setting, where surveillance is not relegated to a change of mean or to normal observations only. Our method of proof relies on asymptotic Bayesian analysis and on renewal theory.

Original languageEnglish
Pages (from-to)1729-1739
Number of pages11
JournalStatistica Sinica
Volume19
Issue number4
StatePublished - Oct 2009

Keywords

  • Changepoint problems
  • Cusum procedures
  • Sequential detection
  • Shiryaev-roberts procedures

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