Optimal estimation of high-dimensional sparse covariance matrices with missing data

Li Miao and Jinru Wang

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 16, 5129-5145

Abstract: Missing data have emerged in broad disciplines such as biology, geophysics, economics, public health, and social science. This article explores the optimal estimation of high-dimensional covariance matrix with missing data over a general sparse space ℋε(cn, p). First, the upper bounds of adaptive entrywise thresholding estimator are proposed. Then the minimax lower bound is established by a simple and effective approach. Finally, numerical simulations and real data analysis demonstrate the advantages of our estimator Σ̂τ over the estimator Σ̂at of Cai and Zhang (2016).

Date: 2025
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DOI: 10.1080/03610926.2024.2434554

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