Sparse covariance matrix estimation in high-dimensional deconvolution

Denis Belomestny (), Mathias Trabs () and Alexandre Tsybakov ()
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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

No 2017-25, Working Papers from Center for Research in Economics and Statistics

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

Keywords: Thresholding; minimax convergence rates; Fourier methods; severely ill-posed inverse problem (search for similar items in EconPapers)
Pages: 32 pages
Date: 2017-10-30
New Economics Papers: this item is included in nep-ecm
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