On robustness of the Shiryaev–Roberts change-point detection procedure under parameter misspecification in the post-change distribution

References

• Basseville, M., Nikiforov, I. V. (1993). Detection of Abrupt Changes: Theory and Application. Englewood Cliffs, NJ: Prentice Hall, Inc., ISBN 0-13-126780-9.
   Google Scholar
• Duncan, A. J. (1956). The economic design of charts used to maintain current control of a process. Journal of the American Statistical Association 51(274):228–242. doi:10.1080/01621459.1956.10501322.
   Google Scholar
• Feinberg, E. A., Shiryaev, A. N. (2006). Quickest detection of drift change for Brownian motion in generalized Bayesian and minimax settings. Statistics & Decisions 24(4):445–470. doi:10.1524/stnd.2006.24.4.445.
   Google Scholar
• Ho, C., Case, K. (1994). Economic design of control charts: A literature review for 1981–1991. Journal of Quality Technology 26(1):39–53.
   Google Scholar
• Kenett, R. S., Pollak, M. (1996). Data-analytic aspects of the Shiryaev–Roberts control chart: Surveillance of a non-homogeneous Poisson process. Journal of Applied Statistics, 23(1):125–138. doi:10.1080/02664769624413.
   Google Scholar
• Knoth, S. (2006). The art of evaluating monitoring schemes—How to measure the performance of control charts? In: Lenz, H.-J., Wilrich, P.-T., eds. Frontiers in Statistical Quality Control 8, Physica-Verlag HD, pp. 74–99. doi:10.1007/3-7908-1687-6_5.
   Google Scholar
• Lorden, G. (1971). Procedures for reacting to a change in distribution. Annals of Mathematical Statistics 42(6):1897–1908. doi:10.1214/aoms/1177693055.
   Google Scholar
• Lorenzen, T. J., Vance, L. C. (1986). The economic design of control charts: A unified approach. Technometrics 28(1):3–10.
   Google Scholar
• Mahmoud, M. A., Woodall, W. H., Davis, R. E. (2008). Performance comparison of some likelihood ratio-based statistical surveillance methods. Journal of Applied Statistics 35(7):783–798. doi:10.1080/02664760802005878.
   Google Scholar
• Montgomery, D. C. (1980). The economic design of control charts: A review and literature survey. Journal of Quality Technology 12(2):75–87.
   Google Scholar
• Moustakides, G. V. (1986). Optimal stopping times for detecting changes in distributions. Annals of Statistics 14(4):1379–1387.
   Google Scholar
• Moustakides, G. V., Polunchenko, A. S., Tartakovsky, A. G. (2009). Numerical comparison of CUSUM and Shiryaev–Roberts procedures for detecting changes in distributions. Communications in Statistics—Theory and Methods 38(16):3225–3239. doi:10.1080/03610920902947774.
   Google Scholar
• Moustakides, G. V., Polunchenko, A. S., Tartakovsky, A. G. (2011). A numerical approach to performance analysis of quickest change-point detection procedures. Statistica Sinica 21(2):571–596.
   Google Scholar
• Page, E. S. (1954). Continuous inspection schemes. Biometrika 41(1):100–115. doi:10.1093/biomet/41.1-2.100.
   Google Scholar
• Pollak, M. (1985). Optimal detection of a change in distribution. Annals of Statistics 13(1):206–227. doi:10.1214/aos/1176346587.
   Google Scholar
• Pollak, M. (1987). Average run lengths of an optimal method of detecting a change in distribution. Annals of Statistics 15(2):749–779. doi:10.1214/aos/1176350373.
   Google Scholar
• Pollak, M. (2009). The Shiryaev–Roberts changepoint detection procedure in retrospect—Theory and practice. In: Proceedings of the 2nd International Workshop in Sequential Methodologies (IWSM’2009), University of Technology of Troyes, Troyes, France.
   Google Scholar
• Pollak, M., Siegmund, D. (1985). A diffusion process and its applications to detecting a change in the drift of Brownian motion. Biometrika 72(2):267–280. doi:10.1093/biomet/72.2.267.
   Google Scholar
• Pollak, M., Tartakovsky, A. G. (2008). Exact optimality of the Shiryaev–Roberts procedure for detecting changes in distributions. In: Proceedings of the 2008 International Symposium on Information Theory and Its Applications (ISITA’2008), Auckland, New Zealand, pp. 1–6. doi:10.1109/ISITA.2008.4895424.
   Google Scholar
• Pollak, M., Tartakovsky, A. G. (2009). Optimality properties of the Shiryaev–Roberts procedure. Statistica Sinica 19(4):1729–1739.
   Google Scholar
• Polunchenko, A. S., Sokolov, G., Du, W. (2013). Quickest change-point detection: A bird's eye view. In: Proceedings of the 2013 Joint Statistical Meetings (JSM’2013), Montréal, Québec, Canada.
   Google Scholar
• Polunchenko, A. S., Sokolov, G., Du, W. (2014a). Efficient performance evaluation of the Generalized Shiryaev–Roberts detection procedure in a multi-cyclic setup. Applied Stochastic Models in Business and Industry 30(6):723–739. doi:10.1002/asmb.2026.
   Google Scholar
• Polunchenko, A. S., Sokolov, G., Du, W. (2014b). An accurate method for determining the pre-change Run Length distribution of the Generalized Shiryaev–Roberts detection procedure. Sequential Analysis 33(1):112–134. doi:10.1080/07474946.2014.856642.
   Google Scholar
• Polunchenko, A. S., Sokolov, G., Tartakovsky, A. G. (2015). Optimal design and analysis of the Exponentially Weighted Moving Average chart for exponential data. Sri Lankan Journal of Applied Statistics 5(4):57–80. doi:10.4038/sljastats.v5i4.7784. Special Issue: Modern Statistical Methodologies in the Cutting Edge of Science.
   Google Scholar
• Polunchenko, A. S., Tartakovsky, A. G. (2012). State-of-the-art in sequential change-point detection. Methodology and Computing in Applied Probability 14(3):649–684. doi:10.1007/s11009-011-9256-5.
   Google Scholar
• Polunchenko, A. S., Tartakovsky, A. G., Mukhopadhyay, N. (2012). Nearly optimal change-point detection with an application to cybersecurity. Sequential Analysis 31(3):409–435. doi:10.1080/07474946.2012.694351.
   Google Scholar
• Poor, H. V., Hadjiliadis, O. (2009). Quickest Detection. New York, NY: Cambridge University Press.
   Google Scholar
• Ritov, Y. (1990). Decision theoretic optimality of the CUSUM procedure. Annals of Statistics 18(3):1464–1469. doi:10.1214/aos/1176347761.
   Google Scholar
• Roberts, S. W. (1959). Control chart tests based on geometric moving averages. Technometrics 1(3):239–250. doi:10.1080/00401706.1959.10489860.
   Google Scholar
• Roberts, S. W. (1966). A comparison of some control chart procedures. Technometrics 8(3):411–430.
   Google Scholar
• Shiryaev, A. N. (1961). The problem of the most rapid detection of a disturbance in a stationary process. Soviet Mathematics—Doklady 2:795–799. Translation from Dokl. Akad. Nauk SSSR 138:1039–1042, 1961.
   Google Scholar
• Shiryaev, A. N. (1963). On optimum methods in quickest detection problems. Theory of Probability and Its Applications 8(1):22–46. doi:10.1137/1108002.
   Google Scholar
• Shiryaev, A. N. (1978). Optimal Stopping Rules. New York, NY: Springer-Verlag.
   Google Scholar
• Shiryaev, A. N. (1995). Probability, Vol. 95, Graduate Texts in Mathematics. 2nd ed. New York, NY: Springer-Verlag.
   Google Scholar
• Shiryaev, A. N. (2002). Quickest detection problems in the technical analysis of the financial data. In: Geman, H., Madan, D., Pliska, S. R., Vorst, T., eds. Mathematical Finance—Bachelier Congress 2000, Springer Finance, Berlin: Springer, pp. 487–521. doi:10.1007/978-3-662-12429-1_22.
   Google Scholar
• Shiryaev, A. N., Zryumov, P. Y. (2010). On the linear and nonlinear generalized Bayesian disorder problem (discrete time case). In: Delbaen, F., Rásonyi, M., Stricker, C. eds. Optimality and Risk—Modern Trends in Mathematical Finance, Berlin: Springer, pp. 227–236. doi:10.1007/978-3-642-02608-9_12.
   Google Scholar
• Srivastava, M., Wu, Y. (1993). Comparison of EWMA, CUSUM and Shiryayev–Roberts procedures for detecting a shift in the mean. Annals of Statistics 21(2):645–670. doi:10.1214/aos/1176349142.
   Google Scholar
• Tartakovsky, A. G., Moustakides, G. V. (2010). State-of-the-art in Bayesian changepoint detection. Sequential Analysis 29(2):125–145. doi:10.1080/07474941003740997.
   Google Scholar
• Tartakovsky, A. G., Nikiforov, I., Basseville, M. (2014). Sequential Analysis: Hypothesis Testing and Changepoint Detection, Vol. 166, Monographs on Statistics and Applied Probability. Boca Raton, FL: CRC Press.
   Google Scholar
• Tartakovsky, A. G., Polunchenko, A. S., Moustakides, G. V. (2009). Design and comparison of Shiryaev–Roberts- and CUSUM-type change-point detection procedures. In: Proceedings of the 2nd International Workshop in Sequential Methodologies (IWSM’2009), University of Technology of Troyes, Troyes, France.
   Google Scholar
• Tartakovsky, A. G., Polunchenko, A. S., Sokolov, G. (2013). Efficient computer network anomaly detection by changepoint detection methods. IEEE Journal of Selected Topics in Signal Processing 7(1):4–11. doi:10.1109/JSTSP.2012.2233713.
   Google Scholar
• Veeravalli, V. V., Banerjee, T. (2013). Quickest change detection. In: Chellappa, R., Theodoridis, S., eds. Academic Press Library in Signal Processing: Array and Statistical Signal Processing, Vol. 3, Oxford, UK: Academic Press, pp. 209–256
   Google Scholar
• Woodroofe, M. (1982). Nonlinear Renewal Theory in Sequential Analysis. Philadelphia, PA: Society for Industrial and Applied Mathematics. ISBN 0-89871-180-0.
   Google Scholar