Hello,

I'm interested in the distribution of the trace of an inverse-Wishart matrix $W_n^{-1}(I,n)$, where $I$ is $n\times n$ identity matrix. More precisely, I seek for an asymptotic estimate (when $n\to\infty$) for a function $f(n)$ such that $Pr[Tr(W)< f(n)]>2/3$, say.

What I've learned so far:

I know the pdf of the eigenvalues of $W$, thus, I could use it to find the bound, but it could be tedious.

A formula for the expectation of $W_n^{-1}(I,m)$ is known, but it does not work for $n=m$ (the expectation is infinite in this case).

This question seems pretty basic, so I expect it should have been considered before, but my google search hasn't revealed any reference on it so far. Could you help me with any?

Thank you,

Alexander.

inverseof a matrix from $W_n(I,n)$. – Alexander Belov Feb 16 '11 at 15:21