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Estimation of sparse covariance matrix via non-convex regularization

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  • Wang, Xin
  • Kong, Lingchen
  • Wang, Liqun

Abstract

Estimation of high-dimensional sparse covariance matrix is one of the fundamental and important problems in multivariate analysis and has a wide range of applications in many fields. This paper presents a novel method for sparse covariance matrix estimation via solving a non-convex regularization optimization problem. We establish the asymptotic properties of the proposed estimator and develop a multi-stage convex relaxation method to find an effective estimator. The multi-stage convex relaxation method guarantees any accumulation point of the sequence generated is a first-order stationary point of the non-convex optimization. Moreover, the error bounds of the first two stage estimators of the multi-stage convex relaxation method are derived under some regularity conditions. The numerical results show that our estimator outperforms the state-of-the-art estimators and has a high degree of sparsity on the premise of its effectiveness.

Suggested Citation

  • Wang, Xin & Kong, Lingchen & Wang, Liqun, 2024. "Estimation of sparse covariance matrix via non-convex regularization," Journal of Multivariate Analysis, Elsevier, vol. 202(C).
    • Handle: RePEc:eee:jmvana:v:202:y:2024:i:c:s0047259x24000010
    DOI: 10.1016/j.jmva.2024.105294
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    References listed on IDEAS

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