High dimensional matrix estimation with unknown variance of the noise
Klopp, Olga (2011), High dimensional matrix estimation with unknown variance of the noise. https://basepub.dauphine.fr/handle/123456789/7822
TypeDocument de travail / Working paper
External document linkhttp://hal.archives-ouvertes.fr/hal-00649437/fr/
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Abstract (EN)We propose a new pivotal method for estimating high-dimensional matrices. Assume that we observe a small set of entries or linear combinations of entries of an unknown matrix $A_0$ corrupted by noise. We propose a new method for estimating $A_0$ which does not rely on the knowledge or an estimation of the standard deviation of the noise $\sigma$. Our estimator achieves, up to a logarithmic factor, optimal rates of convergence under the Frobenius risk and, thus, has the same prediction performance as previously proposed estimators which rely on the knowledge of $\sigma$. Our method is based on the solution of a convex optimization problem which makes it computationally attractive.
Subjects / Keywordsrecovery of the rank; low rank matrix estimation; matrix regression; Matrix completion
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