Sequential Change-Point Detection When the Pre- and Post-Change Parameters are Unknown

Sequential Analysis

Volumn 29, Issue 2, 2010, Pages 162-175

  Lai, Tze Leung ^a   Xing, Haipeng ^b  

^a STANFORD UNIVERSITY   (United States)

^b Stony Brook University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTICALLY OPTIMAL; BAYESIAN; CHANGE POINT DETECTION; DETECTION RULES; EXPONENTIAL FAMILY; FREQUENTIST; MULTIPARAMETERS; PERFORMANCE CRITERION;

STATISTICS;

EID: 77952569086     PISSN: 07474946     EISSN: 15324176     Source Type: Journal    
DOI: 10.1080/07474941003741078     Document Type: Article

References (24)

1. Chan, H. P. and Lai, T. L. (2003). Saddlepoint Approximations and Nonlinear Boundary Crossing Probabilities of Markov Random Walks, Annals of Applied Probability 13: 395-429.
2. Diaconis, P. and Ylvisaker, D. (1979). Conjugate Priors for Exponential Families, Annals of Statistics 7: 269-281.
3. Lai, T. L. (1995). Sequential Changepoint Detection in Quality Control and Dynamical Systems, Journal of Royal Statistical Society, Series B 57: 613-658.
4. Lai, T. L. (1998). Information Bounds and Quick Detection of Parameter Changes in Stochastic Systems, IEEE Transactions on Information Theory 44: 2917-2929.
5. Lai, T. L. (2000). Sequential Multiple Hypothesis Testing and Efficient Fault Detection- isolation in Stochastic Systems, IEEE Transactions on Information Theory 46: 595-608.
6. Lai, T. L. and Chan, H. P. (2008). Discussion on Is Average Run Length to False Alarm Always an Information Criterion? by Yajun Mei, Sequential Analysis 27: 385-388.
7. Lai, T. L. and Xing, H. (2008). A Simple Bayesian Approach to Multiple Change-Points, Technical Report, Department of Statistics, Stanford University.
8. Lai, T. L., Liu, T., and Xing, H. (2009). A Bayesian Approach to Sequential Surveillance in Exponential Families, Communications in Statistics: Theory and Methods (Special issue in honor of Shelemyahu Zacks) 38: 2958-2968.
9. Lorden, G. (1971). Procedures for Reacting to a Change in Distribution, The Annals of Mathematical Statistics 41: 520-527.
10. Lorden, G. and Pollak, M. (2008). Sequential Change-point Detection Procedures that are Nearly Optimal and Computationally Simple, Sequential Analysis 27: 476-512.
11. Mei, Y. (2006). Suboptimal Properties of Page's CUSUM and Shiryaev-Roberts Procedures in Change-Point Problems with Dependent Observations, Statistica Sinica 16: 883-897.
12. Mei, Y. (2008). Is Average Run Length to False Alarm Always an Information Criterion? Sequential Analysis 27: 351-376.
13. Page, E. S. (1954). Continuous Inspection Schemes, Biometrika 41: 100-114.
14. Pollak, M. (1985). Optimal Detection of a Change in Distribution, Annals of Statistics 18: 1464-1469.
15. Pollak, M. and Siegmund, D. (1991). Sequential Detection of a Change in a Normal Mean When the Initial Value is Unknown, Annals of Statistics 19: 394-416.
16. Roberts, S. W. (1966). A Comparison of Some Control Chart Procedures, Technometrics 8: 411-430.
17. Shiryaev, A. N. (1963). On Optimum Methods in Quickest Detection Problems, Theory of Probability and Its Applications 8: 22-46.
18. Shiryaev, A. N. (1978). Optimal Stopping Rules, New York: Springer-Verlag.
19. Siegmund, D. and Venkatraman, E. S. (1995). Using the Generalized Livelihood Ratio Statistic for Sequential Detection of a Change-Point, Annals of Statistics 23: 255-271.
20. Tartakovsky, A. G. (2005). Asymptotic Performance of a Multichart CUSUM Test Under False Alarm Probability Constraint, in Proceedings of the 44th IEEE Conference on Decision and Control and the European Control Conference, pp. 320-325, Seville, Spain, December 12-15.
21. Tartakovsky, A. G. (2008). Discussion on "Is Average Run Length to False Alarm Always an Informative Criterion?" by Yajun Mei, Sequential Analysis 27: 396-405.
22. Woodroofe, M. (1978). Large Deviations of Likelihood Ratio Statistics with Applications to Sequential Testing, Annals of Statistics 6: 72-84.
23. Zacks, S. (1991). Detection and Change-Point Problems, in Handbook of Sequential Analysis, B. K. Ghosh and P. K. San, eds., pp. 531-562, New York: Dekker.
24. Zacks, S. and Barzily, Z. (1981). Bayes Procedures for Detecting a Shift in the Probability of Success in a Series of Bernoulli Trials, Journal of Statistical Planning and Inference 5: 107-119.