IDEAS home Printed from https://ideas.repec.org/a/wsi/apjorx/v32y2015i01ns0217595915400059.html
   My bibliography  Save this article

A Computable Characterization of the Extrinsic Mean of Reflection Shapes and Its Asymptotic Properties

Author

Listed:
  • Chao Ding

    (School of Mathematics, University of Southampton, National Center for Mathematics and Interdisciplinary Sciences, Chinese Academy of Sciences, Southampton SO17 1BJ, United Kingdom)

  • Hou-Duo Qi

    (School of Mathematics, University of Southampton, Southampton SO17 1BJ, United Kingdom)

Abstract

The reflection shapes of configurations in ℜm with k landmarks consist of all the geometric information that is invariant under compositions of similarity and reflection transformations. By considering the corresponding Schoenberg embedding, we embed the reflection shape space into the Euclidean space of all (k - 1) by (k - 1) real symmetric matrices. In this paper, we provide a computable formula of the extrinsic mean of the reflection shapes in arbitrary dimensions. Moreover, the asymptotic analysis of the extrinsic mean of the reflection shapes is studied. By using the differentiability of spectral operators, we obtain a central limit theorem of the sample extrinsic mean of the reflection shapes. As a direct application, the two-example hypothesis test of the reflection shapes is also derived.

Suggested Citation

  • Chao Ding & Hou-Duo Qi, 2015. "A Computable Characterization of the Extrinsic Mean of Reflection Shapes and Its Asymptotic Properties," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 32(01), pages 1-16.
    • Handle: RePEc:wsi:apjorx:v:32:y:2015:i:01:n:s0217595915400059
    DOI: 10.1142/S0217595915400059
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0217595915400059
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0217595915400059?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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:wsi:apjorx:v:32:y:2015:i:01:n:s0217595915400059. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/apjor/apjor.shtml .

    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.