Sparse covariance matrix estimation in high-dimensional deconvolution Article Swipe
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· 2019
· Open Access
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· DOI: https://doi.org/10.3150/18-bej1040a
· OA: W2766248958
We study the estimation of the covariance matrix $Σ$ 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 $Σ$. We establish an oracle inequality for these estimators under model miss-specification and derive non-asymptotic minimax convergence rates that are shown to be logarithmic in $n/\log p$. 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.
