# Sparse covariance matrix estimation in high-dimensional deconvolution

arXiv: https://arxiv.org/abs/1710.10870 · HTML: https://mlsanity.com/paper/1710.10870/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Oct 2017.

## Built on by (most cited first, 2 of 2)

- [Selective inference for k-means clustering](https://mlsanity.com/paper/2203.15267/) (2022)
- [Learning Networks from Gaussian Graphical Models and Gaussian Free Fields](https://mlsanity.com/paper/2308.02344/) (2023)

## Abstract (arXiv)

We study the estimation of the covariance matrix Sigma 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 Sigma. 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.