I would like to make the following statement as true;
Let S represent a (pxp) sample covariance matrix from a finite sample X, (n x p) n< infinity, n>p, from a general (possibly mixed) PDF G(.) with covariance (2nd central moment) V
Then E[inv(S)] = inv(V).*A where .* is the Hadamard product operator (Matlab notation) and
where a(i,j) > 1 (or do I need >=?)
This should follow from Jensen's Inequality if inv(X) is a strictly convex operation on X.
Let S represent a (pxp) sample covariance matrix from a finite sample X, (n x p) n< infinity, n>p, from a general (possibly mixed) PDF G(.) with covariance (2nd central moment) V
Then E[inv(S)] = inv(V).*A where .* is the Hadamard product operator (Matlab notation) and
where a(i,j) > 1 (or do I need >=?)
This should follow from Jensen's Inequality if inv(X) is a strictly convex operation on X.