High Dimensional Matrix Estimation With Unknown Variance Of The Noise

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 A0 corrupted by noise. We propose a new method for estimating A0 which does not rely on the knowledge or an estimation of the standard deviation of the noise . 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 . Our method is based on the solution of a convex optimization problem which makes it computationally attractive