Estimation of Low-Rank Covariance Function

Vald Koltchinskii (), Karim Lounici () and Alexandre Tsybakov ()
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Vald Koltchinskii: Georgia Institute of Technology
Karim Lounici: Georgia Institute of Technology
Alexandre Tsybakov: CREST, ENSAE

No 2016-08, Working Papers from Center for Research in Economics and Statistics

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.

Keywords: Gaussian process; Low rank Covariance Function; Nuclear norm; Empirical risk minimization; Minimax lower bounds; Adaptation (search for similar items in EconPapers)
Pages: 21
Date: 2016-01
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