IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v174y2019ics0047259x19301733.html
   My bibliography  Save this article

Asymptotically optimal pointwise and minimax change-point detection for general stochastic models with a composite post-change hypothesis

Author

Listed:
  • Pergamenchtchikov, Serguei
  • Tartakovsky, Alexander G.

Abstract

A weighted Shiryaev–Roberts change detection procedure is shown to approximately minimize the expected delay to detection as well as higher moments of the detection delay among all change-point detection procedures with the given low maximal local probability of a false alarm within a window of a fixed length in pointwise and minimax settings for general non-i.i.d. data models and for the composite post-change hypothesis when the post-change parameter is unknown. We establish very general conditions for models under which the weighted Shiryaev–Roberts procedure is asymptotically optimal. These conditions are formulated in terms of the rate of convergence in the strong law of large numbers for the log-likelihood ratios between the “change” and “no-change” hypotheses, and we also provide sufficient conditions for a large class of ergodic Markov processes. Examples related to multivariate Markov models where these conditions hold are given.

Suggested Citation

  • Pergamenchtchikov, Serguei & Tartakovsky, Alexander G., 2019. "Asymptotically optimal pointwise and minimax change-point detection for general stochastic models with a composite post-change hypothesis," Journal of Multivariate Analysis, Elsevier, vol. 174(C).
    • Handle: RePEc:eee:jmvana:v:174:y:2019:i:c:s0047259x19301733
    DOI: 10.1016/j.jmva.2019.104541
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X19301733
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2019.104541?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Serguei Pergamenchtchikov & Alexander G. Tartakovsky, 2018. "Asymptotically optimal pointwise and minimax quickest change-point detection for dependent data," Statistical Inference for Stochastic Processes, Springer, vol. 21(1), pages 217-259, April.
    2. Galtchouk, L. & Pergamenshchikov, S., 2013. "Uniform concentration inequality for ergodic diffusion processes observed at discrete times," Stochastic Processes and their Applications, Elsevier, vol. 123(1), pages 91-109.
    3. Paul D. Feigin & Richard L. Tweedie, 1985. "Random Coefficient Autoregressive Processes:A Markov Chain Analysis Of Stationarity And Finiteness Of Moments," Journal of Time Series Analysis, Wiley Blackwell, vol. 6(1), pages 1-14, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Pergamenchtchikov, Serguei M. & Tartakovsky, Alexander G. & Spivak, Valentin S., 2022. "Minimax and pointwise sequential changepoint detection and identification for general stochastic models," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    2. Bouzebda, Salim & Ferfache, Anouar Abdeldjaoued, 2023. "Asymptotic properties of semiparametric M-estimators with multiple change points," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
    3. Savas Dayanik & Kazutoshi Yamazaki, 2022. "Detection and identification of changes of hidden Markov chains: asymptotic theory," Statistical Inference for Stochastic Processes, Springer, vol. 25(2), pages 261-301, July.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Serguei Pergamenchtchikov & Alexander G. Tartakovsky, 2018. "Asymptotically optimal pointwise and minimax quickest change-point detection for dependent data," Statistical Inference for Stochastic Processes, Springer, vol. 21(1), pages 217-259, April.
    2. Pergamenchtchikov, Serguei M. & Tartakovsky, Alexander G. & Spivak, Valentin S., 2022. "Minimax and pointwise sequential changepoint detection and identification for general stochastic models," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    3. Paul D. Feigin, 2020. "Correction to: Random Coefficient Autoregressive Processes: a Markov Chain Analysis of Stationarity and Finiteness of Moments by Paul D. Feigin and Richard L. Tweedie J. Time Series Anal., Vol. 6, No.," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(6), pages 899-900, November.
    4. Aue, Alexander, 2004. "Strong approximation for RCA(1) time series with applications," Statistics & Probability Letters, Elsevier, vol. 68(4), pages 369-382, July.
    5. Jentsch, Carsten & Subba Rao, Suhasini, 2015. "A test for second order stationarity of a multivariate time series," Journal of Econometrics, Elsevier, vol. 185(1), pages 124-161.
    6. Hwang, S.Y. & Basawa, I.V., 2009. "Branching Markov processes and related asymptotics," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1155-1167, July.
    7. Feike C. Drost & Ramon Van Den Akker & Bas J. M. Werker, 2008. "Local asymptotic normality and efficient estimation for INAR(p) models," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(5), pages 783-801, September.
    8. Federico M Bandi & Valentina Corradi & Daniel Wilhelm, 2016. "Possibly Nonstationary Cross-Validation," CeMMAP working papers 11/16, Institute for Fiscal Studies.
    9. Nedeljkovic, Milan, 2008. "Testing for Smooth Transition Nonlinearity in Adjustments of Cointegrating Systems," The Warwick Economics Research Paper Series (TWERPS) 876, University of Warwick, Department of Economics.
    10. Savas Dayanik & Kazutoshi Yamazaki, 2022. "Detection and identification of changes of hidden Markov chains: asymptotic theory," Statistical Inference for Stochastic Processes, Springer, vol. 25(2), pages 261-301, July.
    11. Aknouche, Abdelhakim & Gouveia, Sonia & Scotto, Manuel, 2023. "Random multiplication versus random sum: auto-regressive-like models with integer-valued random inputs," MPRA Paper 119518, University Library of Munich, Germany, revised 18 Dec 2023.
    12. Knight John & Satchell Stephen, 2011. "Some New Results for Threshold AR(1) Models," Journal of Time Series Econometrics, De Gruyter, vol. 3(2), pages 1-42, April.
    13. Ling, Shiqing & McAleer, Michael, 2002. "NECESSARY AND SUFFICIENT MOMENT CONDITIONS FOR THE GARCH(r,s) AND ASYMMETRIC POWER GARCH(r,s) MODELS," Econometric Theory, Cambridge University Press, vol. 18(3), pages 722-729, June.
    14. Hwang, S. Y. & Woo, Mi-Ja, 2001. "Threshold ARCH(1) processes: asymptotic inference," Statistics & Probability Letters, Elsevier, vol. 53(1), pages 11-20, May.
    15. Hwang, S.Y. & Basawa, I.V., 2011. "Asymptotic optimal inference for multivariate branching-Markov processes via martingale estimating functions and mixed normality," Journal of Multivariate Analysis, Elsevier, vol. 102(6), pages 1018-1031, July.
    16. Leonid I. Galtchouk & Serge M. Pergamenshchikov, 2022. "Adaptive efficient analysis for big data ergodic diffusion models," Statistical Inference for Stochastic Processes, Springer, vol. 25(1), pages 127-158, April.
    17. An, Hongzhi & Chen, Min & Huang, Fuchun, 1997. "The geometric ergodicity and existence of moments for a class of non-linear time series model," Statistics & Probability Letters, Elsevier, vol. 31(3), pages 213-224, January.
    18. Andreas Hetland, 2018. "The Stochastic Stationary Root Model," Econometrics, MDPI, vol. 6(3), pages 1-33, August.
    19. Alexander G. Tartakovsky, 2023. "Quick and Complete Convergence in the Law of Large Numbers with Applications to Statistics," Mathematics, MDPI, vol. 11(12), pages 1-30, June.
    20. Liu, Ji-Chun, 2012. "Structure of a double autoregressive process driven by a hidden Markov chain," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1468-1473.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:174:y:2019:i:c:s0047259x19301733. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.