Minimax optimality of the Shiryayev-Roberts change-point detection rule

D. O. Siegmund*, B. Yakir

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

The result of Pollak [1985. Optimal detection of a change in distribution. Ann. Statist. 13, 206-227] proving the asymptotic optimality in sequential change-point detection of a suitable Shirayayev-Roberts stopping rule up to terms that vanish in the limit is generalized from the case of two completely specified distributions to that of a composite alternative hypothesis in a multidimensional exponential family. An explicit asymptotic lower bound on the expected Kullback-Leibler information required to detect a change-point is derived and is shown to be attained by a Shirayayev-Roberts stopping rule.

Original languageAmerican English
Pages (from-to)2815-2825
Number of pages11
JournalJournal of Statistical Planning and Inference
Volume138
Issue number9
DOIs
StatePublished - 1 Sep 2008

Bibliographical note

Funding Information:
This work have been supported by the NSF and the US-Israel Binational Science Foundation.

Keywords

  • Change-point
  • Minimax optimality
  • Sequential detection

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