High dimensional matrix estimation with unknown variance of the noise

Details High dimensional matrix estimation with unknown variance of the noise High dimensional matrix estimation with unknown variance of the noise

2011-12-13

arxiv.org/abs/1112.3055v2

Mathematics

Statistics Theory

Scientific paper

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.

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