Integration of invariant matrices and application to statistics
Statistics Theory
2016-09-06 v1 Probability
Statistics Theory
Abstract
We consider random matrices that have invariance properties under the action of unitary groups (either a left-right invariance, or a conjugacy invariance), and we give formulas for moments in terms of functions of eigenvalues. Our main tool is the Weingarten calculus. As an application to statistics, we obtain new formulas for the pseudo inverse of Gaussian matrices and for the inverse of compound Wishart matrices.
Cite
@article{arxiv.1205.0956,
title = {Integration of invariant matrices and application to statistics},
author = {Benoit Collins and Sho Matsumoto and Nadia Saad},
journal= {arXiv preprint arXiv:1205.0956},
year = {2016}
}
Comments
19 pages