IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v53y2001i1p67-77.html
   My bibliography  Save this article

Bonferroni-type inequalities for conditional scan statistics

Author

Listed:
  • Chen, Jie
  • Glaz, Joseph
  • Naus, Joseph
  • Wallenstein, Sylvan

Abstract

Scan statistics have been extensively used in many areas of science to analyze the occurrence of observed clusters of events in time or space. Since the scan statistics are based on the highly dependent consecutive subsequences of observed data, accurate probability inequalities for their distributions are of great value. We derive accurate second-order Bonferroni-type inequalities for the distribution of linear and circular scan statistics. Our approach is based on the scanning window representation of scan statistics. Both the one-dimensional continuous and discrete cases are investigated. Based on the numerical results presented in this article, it is evident that the Bonferroni-type inequalities are tight. For all practical purposes, they determine the scan statistics probabilities used in testing. Based on the probability inequalities for the distribution of scan statistics accurate inequalities for the expected size of a possible cluster are derived. Numerical results presented in this article indicate that these inequalities are tight; thus, providing valuable information on the expected size of the largest cluster of events.

Suggested Citation

  • Chen, Jie & Glaz, Joseph & Naus, Joseph & Wallenstein, Sylvan, 2001. "Bonferroni-type inequalities for conditional scan statistics," Statistics & Probability Letters, Elsevier, vol. 53(1), pages 67-77, May.
    • Handle: RePEc:eee:stapro:v:53:y:2001:i:1:p:67-77
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(01)00034-7
    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. Glaz, Joseph, 1992. "Approximations for tail probabilities and moments of the scan statistic," Computational Statistics & Data Analysis, Elsevier, vol. 14(2), pages 213-227, August.
    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. Mohamed-Salem Ahmed & Lionel Cucala & Michaël Genin, 2021. "Spatial autoregressive models for scan statistic," Journal of Spatial Econometrics, Springer, vol. 2(1), pages 1-20, December.

    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. Xiaoping Su & Sylvan Wallenstein & David Bishop, 2001. "Nonoverlapping Clusters: Approximate Distribution and Application to Molecular Biology," Biometrics, The International Biometric Society, vol. 57(2), pages 420-426, June.
    2. Glaz, Joseph & Zhang, Zhenkui, 2006. "Maximum scan score-type statistics," Statistics & Probability Letters, Elsevier, vol. 76(13), pages 1316-1322, July.
    3. Huffer, Fred W. & Chien-Tai Lin, 1997. "Computing the exact distribution of the extremes of sums of consecutive spacings," Computational Statistics & Data Analysis, Elsevier, vol. 26(2), pages 117-132, December.
    4. Anthony Cheng & Disheng Mao & Yuping Zhang & Joseph Glaz & Zhengqing Ouyang, 2023. "Translocation detection from Hi‐C data via scan statistics," Biometrics, The International Biometric Society, vol. 79(2), pages 1306-1317, June.

    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:stapro:v:53:y:2001:i:1:p:67-77. 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.