IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v51y1994i2p338-351.html
   My bibliography  Save this article

An Extension of the Csörgo-Horváth Functional Limit Theorem and Its Applications to Changepoint Problems

Author

Listed:
  • Ferger, D.

Abstract

Consider a triangular array Xn1, ..., Xnn, n[set membership, variant] 1, of rowwise independent random elements with values in a measurable space. Suppose there exists [theta] [set membership, variant] [0, 1)such that Xn1, ..., Xn[n[theta] ] have distribution [nu]1 and Xn[n[theta]] + 1(n), ..., Xnn have distribution [nu]2. Csörgo and Horváth derived an invariance principle for a one-time parameter process, which is the foundation of a test for H0: [theta] = 0 versus H1: [theta] [set membership, variant](0, 1). We are interested in the more complex test problem H0: [theta] [set membership, variant] [Theta]0 versus H1,: [theta] [set membership, variant] [Theta]0, where [Theta]0[subset, double equals](0, 1). To treat this new situation, we extend the Csörgo-Horváth result in proving a functional limit theorem for a suitable two-time parameter process. We briefly sketch several applications of our result. Especially, the power of the Csörgo-Horváth test is investigated in detail.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:51:y:1994:i:2:p:338-351
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(84)71066-9
    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.

    Citations

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


    Cited by:

    1. Gombay, Edit, 2001. "U-Statistics for Change under Alternatives," Journal of Multivariate Analysis, Elsevier, vol. 78(1), pages 139-158, July.
    2. 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.
    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. Steland Ansgar, 2003. "NP-Optimal Kernels for Nonparametric Sequential Detection Rules," Stochastics and Quality Control, De Gruyter, vol. 18(2), pages 149-163, January.

    More about this item

    Statistics

    Access and download statistics

    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:51:y:1994:i:2:p:338-351. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.