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

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  • Zeyu Wu

    (Shanghai Jiao Tong University)

  • Cheng Wang

    (Shanghai Jiao Tong University)

  • Weidong Liu

    (Shanghai Jiao Tong University)

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.

Suggested Citation

  • Zeyu Wu & Cheng Wang & Weidong Liu, 2023. "A unified precision matrix estimation framework via sparse column-wise inverse operator under weak sparsity," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(4), pages 619-648, August.
    • Handle: RePEc:spr:aistmt:v:75:y:2023:i:4:d:10.1007_s10463-022-00856-0
    DOI: 10.1007/s10463-022-00856-0
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    References listed on IDEAS

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