IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v59y1996i2p217-229.html
   My bibliography  Save this article

Effects of Smoothing on Multivariate Statistical Properties of the Normal to a Rough Curve or Surface

Author

Listed:
  • Fisher, Nicholas I.
  • Hall, Peter
  • Kirk, David J.

Abstract

Much of the practical interest attached to curves and surfaces derives from features of roughness, rather than smoothness. For example, considerable attention has been paid to fractal models of curves and surfaces, for which the notions of a normal and curvature are usually not well defined. Nevertheless, these quantities are sometimes measurable, because the device for recording a rough surface (such as a stylus or "compass") adds its own intrinsic smoothness. In this paper we address the effect of such smoothing operations on the multivariate statistical properties of a normal to the surface. Particular attention is paid to the validity of commonly assumed unimodal approximations to the distribution of the normal. It is shown that the actual distribution may have more than one mode, although in a range of situations the unimodal approximation is valid.

Suggested Citation

  • Fisher, Nicholas I. & Hall, Peter & Kirk, David J., 1996. "Effects of Smoothing on Multivariate Statistical Properties of the Normal to a Rough Curve or Surface," Journal of Multivariate Analysis, Elsevier, vol. 59(2), pages 217-229, November.
  • Handle: RePEc:eee:jmvana:v:59:y:1996:i:2:p:217-229
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(96)90062-7
    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.

    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:59:y:1996:i:2:p:217-229. 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: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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 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.

    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.