IDEAS home Printed from
   My bibliography  Save this article

Simple graphs and bounds for the elements of the hat matrix


  • Yadolah Dodge
  • Ali Hadi


In regression analysis, the matrix H = X (XTX)-1XT is known as the 'hat' or 'projection' matrix, among other names. It has been studied by many authors from different perspectives. The main area of study has been the type of measure best adapted to detect leverage points in linear regression. For computational reasons, these measures were originally based on the diagonal elements of the hat matrix. In the present paper, we propose a very simple procedure for identifying leverage groups. The procedure is based on upper and lower bounds for the diagonal and the off-diagonal elements of H. These upper and lower bounds can easily be shown on an index plot of the elements of H.

Suggested Citation

  • Yadolah Dodge & Ali Hadi, 1999. "Simple graphs and bounds for the elements of the hat matrix," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(7), pages 817-823.
  • Handle: RePEc:taf:japsta:v:26:y:1999:i:7:p:817-823
    DOI: 10.1080/02664769922052

    Download full text from publisher

    File URL:
    Download Restriction: Access to full text is restricted to subscribers.

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

    References listed on IDEAS

    1. Dodge, Yadolah, 1997. "LAD Regression for Detecting Outliers in Response and Explanatory Variables," Journal of Multivariate Analysis, Elsevier, vol. 61(1), pages 144-158, April.
    Full references (including those not matched with items on IDEAS)

    More about this item


    Access and download statistics


    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:taf:japsta:v:26:y:1999:i:7:p:817-823. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Chris Longhurst). General contact details of provider: .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.