A unified precision matrix estimation framework via sparse column-wise inverse operator under weak sparsity

Zeyu Wu, Cheng Wang () and Weidong Liu
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Zeyu Wu: Shanghai Jiao Tong University
Cheng Wang: Shanghai Jiao Tong University
Weidong Liu: Shanghai Jiao Tong University

Annals of the Institute of Statistical Mathematics, 2023, vol. 75, issue 4, No 4, 619-648

Abstract: Abstract In this paper, we estimate the high-dimensional precision matrix under the weak sparsity condition where many entries are nearly zero. We revisit the sparse column-wise inverse operator estimator and derive its general error bounds under the weak sparsity condition. A unified framework is established to deal with various cases including the heavy-tailed data, the non-paranormal data, and the matrix variate data. These new methods can achieve the same convergence rates as the existing methods and can be implemented efficiently.

Keywords: Gaussian graphical model; High-dimensional data; Lasso; Precision matrix; Weak sparsity (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10463-022-00856-0

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