IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v78y2001i1p139-158.html
   My bibliography  Save this article

U-Statistics for Change under Alternatives

Author

Listed:
  • Gombay, Edit

Abstract

Asymptotic distributions of U-statistics to test for possible changes in the distribution will be derived when the change occurred. We will show that for all possible types of kernels, symmetric, antisymmetric, degenerate, non-degenerate, the test statistics are asymptotically normally distributed. We also study the distribution of the estimator of the time of change. Its large sample behaviour is approximately that of the maximum of a two-sided random walk. The terms in these random walks explain the exact nature of bias in the change-point estimator. Several examples will be given as illustration.

Suggested Citation

  • Gombay, Edit, 2001. "U-Statistics for Change under Alternatives," Journal of Multivariate Analysis, Elsevier, vol. 78(1), pages 139-158, July.
    • Handle: RePEc:eee:jmvana:v:78:y:2001:i:1:p:139-158
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(00)91945-6
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Hall, Peter, 1979. "On the invariance principle for U-statistics," Stochastic Processes and their Applications, Elsevier, vol. 9(2), pages 163-174, November.
    2. Ferger, Dietmar & Stute, Winfried, 1992. "Convergence of changepoint estimators," Stochastic Processes and their Applications, Elsevier, vol. 42(2), pages 345-351, September.
    3. Dietmar Ferger, 1994. "On the power of nonparametric changepoint-tests," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 41(1), pages 277-292, December.
    4. Csörgo, Miklós & Horváth, Lajos, 1988. "Invariance principles for changepoint problems," Journal of Multivariate Analysis, Elsevier, vol. 27(1), pages 151-168, October.
    5. Ferger, D., 1994. "An Extension of the Csörgo-Horváth Functional Limit Theorem and Its Applications to Changepoint Problems," Journal of Multivariate Analysis, Elsevier, vol. 51(2), pages 338-351, November.
    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. Cho, Haeran & Kirch, Claudia, 2024. "Data segmentation algorithms: Univariate mean change and beyond," Econometrics and Statistics, Elsevier, vol. 30(C), pages 76-95.
    2. Dominique Guegan, 2007. "Global and local stationary modelling in finance: theory and empirical evidence," Post-Print halshs-00187875, HAL.
    3. Alfredas Račkauskas & Martin Wendler, 2020. "Convergence of U-processes in Hölder spaces with application to robust detection of a changed segment," Statistical Papers, Springer, vol. 61(4), pages 1409-1435, August.
    4. Lajos Horváth & Gregory Rice, 2014. "Extensions of some classical methods in change point analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 219-255, June.

    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. Steland Ansgar, 2003. "NP-Optimal Kernels for Nonparametric Sequential Detection Rules," Stochastics and Quality Control, De Gruyter, vol. 18(2), pages 149-163, January.
    2. Natalie Neumeyer & Ingrid Van Keilegom, 2009. "Change‐Point Tests for the Error Distribution in Non‐parametric Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(3), pages 518-541, September.
    3. Zhang, Hanqin, 2000. "On a weighted embedding for generalized pontograms," Stochastic Processes and their Applications, Elsevier, vol. 88(2), pages 213-224, August.
    4. Ansgar Steland, 2005. "Random Walks with Drift – A Sequential Approach," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(6), pages 917-942, November.
    5. Rukhin, Andrew L., 1996. "The rates of convergence of Bayes estimators in change-point analysis," Statistics & Probability Letters, Elsevier, vol. 27(4), pages 319-329, May.
    6. Alfredas Račkauskas & Martin Wendler, 2020. "Convergence of U-processes in Hölder spaces with application to robust detection of a changed segment," Statistical Papers, Springer, vol. 61(4), pages 1409-1435, August.
    7. Venkata Jandhyala & Stergios Fotopoulos & Ian MacNeill & Pengyu Liu, 2013. "Inference for single and multiple change-points in time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(4), pages 423-446, July.
    8. Cho, Haeran & Kirch, Claudia, 2024. "Data segmentation algorithms: Univariate mean change and beyond," Econometrics and Statistics, Elsevier, vol. 30(C), pages 76-95.
    9. Maria Mohr & Leonie Selk, 2020. "Estimating change points in nonparametric time series regression models," Statistical Papers, Springer, vol. 61(4), pages 1437-1463, August.
    10. Steland Ansgar, 2003. "Jump-preserving monitoring of dependent time series using pilot estimators," Statistics & Risk Modeling, De Gruyter, vol. 21(4), pages 343-366, April.
    11. Holmes, Mark & Kojadinovic, Ivan & Quessy, Jean-François, 2013. "Nonparametric tests for change-point detection à la Gombay and Horváth," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 16-32.
    12. Olmo Jose & Pouliot William, 2011. "Early Detection Techniques for Market Risk Failure," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 15(4), pages 1-55, September.
    13. M. Denker & C. Grillenberger & G. Keller, 1985. "A note on invariance principles for v. Mises' statistics," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 32(1), pages 197-214, December.
    14. Lee, Chung-Bow, 1996. "Nonparametric multiple change-point estimators," Statistics & Probability Letters, Elsevier, vol. 27(4), pages 295-304, May.
    15. Kasprzak, Mikołaj J., 2020. "Stein’s method for multivariate Brownian approximations of sums under dependence," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 4927-4967.
    16. Jose Olmo & William Pouliot, 2014. "Tests to Disentangle Breaks in Intercept from Slope in Linear Regression Models with Application to Management Performance in the Mutual Fund Industry," Discussion Papers 14-02, Department of Economics, University of Birmingham.
    17. Emad-Eldin Aly & Subhash Kochar, 1997. "Change point tests based on U-statistics with applications in reliability," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 45(1), pages 259-269, January.

    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:78:y:2001:i:1:p:139-158. 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.