All Invariant Moments of the Wishart Distribution

Gérard Letac and Hélène Massam

Scandinavian Journal of Statistics, 2004, vol. 31, issue 2, 295-318

Abstract: Abstract. In this paper, we compute moments of a Wishart matrix variate U of the form 𝔼(Q(U)) where Q(u) is a polynomial with respect to the entries of the symmetric matrix u, invariant in the sense that it depends only on the eigenvalues of the matrix u. This gives us in particular the expected value of any power of the Wishart matrix U or its inverse U− 1. For our proofs, we do not rely on traditional combinatorial methods but rather on the interplay between two bases of the space of invariant polynomials in U. This means that all moments can be obtained through the multiplication of three matrices with known entries. Practically, the moments are obtained by computer with an extremely simple Maple program.

Date: 2004
References: View complete reference list from CitEc
Citations: View citations in EconPapers (19)

Downloads: (external link)
https://doi.org/10.1111/j.1467-9469.2004.01-043.x

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:scjsta:v:31:y:2004:i:2:p:295-318

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0303-6898

Access Statistics for this article

Scandinavian Journal of Statistics is currently edited by ÿrnulf Borgan and Bo Lindqvist

More articles in Scandinavian Journal of Statistics from Danish Society for Theoretical Statistics, Finnish Statistical Society, Norwegian Statistical Association, Swedish Statistical Association
Bibliographic data for series maintained by Wiley Content Delivery ().