Optimality properties of the shiryaev-roberts procedure

Statistica Sinica

Volumn 19, Issue 4, 2009, Pages 1729-1739

  Pollak, Moshe ^a   Tartakovsky, Alexander G ^b  

^a HEBREW UNIVERSITY OF JERUSALEM   (Israel)

^b UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

Author keywords

Changepoint problems; Cusum procedures; Sequential detection; Shiryaev roberts procedures

Indexed keywords

EID: 70249085400     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (19)

1. Beibel, M. (1996). A note on Ritov's Bayes approach to the minimax property of the Cusum procedure. Ann. Statist. 24, 1804-1812.
2. Feinberg, E. A. and Shiryaev, A. N. (2006). Quickest detection of drift change for Brownian motion in generalized Bayesian and minimax settings. Statist. Decisions 24, 445-470.
3. Feller, W. (1966). An Introduction to Probability Theory and Its Applications. Vol. II, Wiley, New York.
4. Lorden, G. (1971). Procedures for reacting to a change in distribution. Ann. Math. Statist. 42, 1897-1908.
5. Moustakides, G. V. (1986). Optimal stopping times for detecting changes in distributions. Ann. Statist. 14, 1379-1387.
6. Page, E. S. (1954). Continuous inspection schemes. Biometrika 41, 100-115.
7. Pollak, M. (1985). Optimal detection of a change in distribution. Ann. Statist. 13, 206-227.
8. Pollak, M. (1987). Average run lengths of an optimal method of detecting a change in distribution. Ann. Statist. 15, 749-779.
9. Pollak, M. and Tartakovsky, A. G. (2008). Asymptotic exponentiality of the distribution of first exit times for a class of Markov processes with applications to quickest change detection. Teoriya Veroyatn. Primen. 53, 500-515.
10. Ritov, Y. (1990). Decision theoretic optimality of the Cusum procedure. Ann. Statist. 18, 1466- 1469.
11. Roberts, S. W. (1966). A comparison of some control chart procedures. Technometrics 8, 411- 430.
12. Shiryaev, A. N. (1961). The problem of the most rapid detection of a disturbance in a stationary process. Soviet Math. Dokl. 2, 795-799 (translation from Dokl. Akad. Nauk SSSR 138, 1039-1042, 1961).
13. Shiryaev, A. N. (1963). On optimum methods in quickest detection problems. Theory Probab. Appl. 8, 22-46.
14. Shiryaev, A. N. (1978). Optimal Stopping Rules. Springer-Verlag, New York.
15. Shiryaev, A. N. (1996). Minimax optimality of the method of cumulative sum (cusum) in the case of continuous time. Russian Math. Surveys 51, 750-751.
16. Tartakovsky, A. G. (1991). Sequential Methods in the Theory of Information Systems. Radio i Svyaz', Moscow (in Russian).
17. Tartakovsky, A. G., Rozovskii, B. L., Blazek, R. and Kim, H. (2006). Detection of intrusions in information systems by sequential change-point methods (with discussion). Statistical Methodology 3, 252-340.
18. Tartakovsky, A. G. and Veeravalli, V. V. (2004). Change-point detection in multichannel and distributed systems with applications. In Applications of Sequential Methodologies (Edited by N. Mukhopadhyay, S. Datta and S. Chattopadhyay), 331-363. Marcel Dekker, Inc., New York.
19. Yakir, B. (1995). A note on the run length to false alarm of a change-point detection policy. Ann. Statist. 23, 272-281.