IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v11y1981i3p418-433.html
   My bibliography  Save this article

Eigenfunctions of expected value operators in the Wishart distribution, II

Author

Listed:
  • Kushner, H. B.
  • Lebow, Arnold
  • Meisner, Morris

Abstract

Let V = (vij) denote the k - k symmetric scatter matrix following the Wishart distribution W(k, n, [Sigma]). The problem posed is to characterize the eigenfunctions of the expectation operators of the Wishart distribution, i.e., those scalar-valued functions f(V) such that (Enf)(V) = [lambda]n,kf(V). A finite sequence of polynomial eigenspaces, EP spaces, exists whose direct sum is the space of all homogeneous polynomials. These EP subspaces are invariant and irreducible under the action of the congruence transformation V --> T'VT. Each of these EP subspaces contains an orthogonally invariant subspace of dimension one. The number of EP subspaces is determined and eigenvalues are computed. Bi-linear expansions of I + VA-n/2 and (tr VA)r into eigenfunctions are given. When f(V) is an EP polynomial, then f(V-1) is an EP function. These EP subspaces are identical to the more abstractly defined polynomial subspaces studied by James.

Suggested Citation

  • Kushner, H. B. & Lebow, Arnold & Meisner, Morris, 1981. "Eigenfunctions of expected value operators in the Wishart distribution, II," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 418-433, September.
    • Handle: RePEc:eee:jmvana:v:11:y:1981:i:3:p:418-433
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0047-259X(81)90085-3
    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:11:y:1981:i:3:p:418-433. 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.