Integration of invariant matrices and application to statistics
arXiv:1205.0956 · doi:10.1016/j.jmva.2013.12.011
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.
19 pages
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- Analysis of Bayesian Inference Algorithms by the Dynamical Functional Approach
- Compound Wishart Matrices and Noisy Covariance Matrices: Risk Underestimation