unpublished

Joel Bun and Romain Allez and Jean-Philippe Bouchaud and Marc Potters


Finance Group (2015) : Rotational invariant estimator for general noisy matrices




Rotational invariant estimator for general noisy matrices

Joel Bun and Romain Allez and Jean-Philippe Bouchaud and Marc Potters




unpublished

We investigate the problem of estimating a given real symmetric signal matrix C from a noisy observation matrix M in the limit of large dimension. We consider the case where the noisy measurement M comes either from an arbitrary additive or multiplicative rotational invariant perturbation. We establish, using the Replica method, the asymptotic global law estimate for three general classes of noisy matrices, significantly extending previously obtained results. We give exact results concerning the asymptotic deviations (called overlaps) of the perturbed eigenvectors away from the true ones, and we explain how to use these overlaps to "clean" the noisy eigenvalues of M. We provide some numerical checks for the different estimators proposed in this paper and we also make the connection with some well known results of Bayesian statistics.

To cite this publication :


Joel Bun, Romain Allez, Jean-Philippe Bouchaud, Marc Potters: Rotational invariant estimator for general noisy matrices. 2015.





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