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High Dimensional Matrix Estimation With Unknown Variance Of The Noise

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  • Olga Klopp

    (CREST)

Abstract

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

Suggested Citation

  • Olga Klopp, 2012. "High Dimensional Matrix Estimation With Unknown Variance Of The Noise," Working Papers 2012-05, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2012-05
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    References listed on IDEAS

    as
    1. A. Belloni & V. Chernozhukov & L. Wang, 2011. "Square-root lasso: pivotal recovery of sparse signals via conic programming," Biometrika, Biometrika Trust, vol. 98(4), pages 791-806.
    2. Angelika Rohde & Alexandre Tsybakov, 2010. "Estimation on High-dimensional Low Rank Matrices," Working Papers 2010-25, Center for Research in Economics and Statistics.
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    Keywords

    Matrix completion; matrix regression; low rank matrix estimation; recovery of the rank;
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