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Estimation of Low-Rank Covariance Function

Author

Listed:
  • Vald Koltchinskii

    (Georgia Institute of Technology)

  • Karim Lounici

    (Georgia Institute of Technology)

  • Alexandre Tsybakov

    (CREST, ENSAE)

Abstract

We consider the problem of estimating a low rank covariance function K(t, u) of a Gaussian process S(t); t [0; 1] based on n i.i.d. copies of S observed in a white noise. We suggest a new estimation procedure adapting simultaneously to the low rank structure and the smoothness of the covariance function. The new procedure is based on nuclear norm penalization and exhibits superior performances as compared to the sample covariance function by a polynomial factor in the sample size n. Other results include a minimax lower bound for estimation of low-rank covariance functions showing that our procedure is optimal as well as a scheme to estimate the unknown noise variance of the Gaussian process.

Suggested Citation

  • Vald Koltchinskii & Karim Lounici & Alexandre Tsybakov, 2016. "Estimation of Low-Rank Covariance Function," Working Papers 2016-08, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2016-08
    as

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    References listed on IDEAS

    as
    1. Yao, Fang & Muller, Hans-Georg & Wang, Jane-Ling, 2005. "Functional Data Analysis for Sparse Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 577-590, June.
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