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Sparse covariance matrix estimation in high-dimensional deconvolution

Author

Listed:
  • Denis Belomestny

    (Duisburg-Essen University, Faculty of Mathematics, National Research University Higher School of Economics)

  • Mathias Trabs

    (Universität Hamburg; Faculty of Mathematics)

  • Alexandre Tsybakov

    (CREST;ENSAE)

Abstract

We study the estimation of the covariance matrix _ of a p-dimensional normal random vector based on n independent observations corrupted by additive noise. Only a general nonparametric assumption is imposed on the distribution of the noise without any sparsity constraint on its covariance matrix. In this high-dimensional semiparametric deconvolution problem, we propose spectral thresholding estimators that are adaptive to the sparsity of _. We establish an oracle inequality for these estimators under model missspecification and derive non-asymptotic minimax convergence rates that are shown to be logarithmic in log p/n. We also discuss the estimation of low-rank matrices based on indirect observations as well as the generalization to elliptical distributions. The finite sample performance of the threshold estimators is illustrated in a numerical example. ;Classification-JEL: Primary 62H12; secondary 62F12, 62G05

Suggested Citation

  • Denis Belomestny & Mathias Trabs & Alexandre Tsybakov, 2017. "Sparse covariance matrix estimation in high-dimensional deconvolution," Working Papers 2017-25, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2017-25
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    References listed on IDEAS

    as
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    Keywords

    Thresholding; minimax convergence rates; Fourier methods; severely ill-posed inverse problem;
    All these keywords.

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