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Articles (2017), Statistica Sinica, 27 (1), pp. 115-145

High dimensional matrix estimation with unknown variance of the noise

Klopp Olga , Gaiffas Stefano

Assume that we observe a small set of entries or linear combinations of entries of an unknown matrix A corrupted by noise. We propose a new method for estimating A which does not rely on the knowledge or on an estimation of the standard deviation of the noise s. 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 s. Some numerical experiments show the benefits of this approach. Lien vers l'article

KLOPP, O. and GAIFFAS, S. (2017). High dimensional matrix estimation with unknown variance of the noise. Statistica Sinica, 27(1), pp. 115-145.