Affordable Access

All Invariant Moments of the Wishart Distribution

Authors
Disciplines
  • Mathematics

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"-super- -  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. Copyright 2004 Board of the Foundation of the Scandinavian Journal of Statistics..

There are no comments yet on this publication. Be the first to share your thoughts.

Statistics

Seen <100 times
0 Comments

More articles like this

Integration of invariant matrices and moments of i...

on Journal of Multivariate Analys...

Integration of invariant matrices and moments of i...

on Journal of Multivariate Analys...

MacMahon's Master Theorem, Representation Theory,...

on Advances in Applied Mathematic...

The distribution and moments of the smallest eigen...

on Linear Algebra and its Applica... Jan 01, 1991
More articles like this..