High-Dimensional Covariance Estimation via Constrained L q -Type Regularization

Xin Wang (), Lingchen Kong, Liqun Wang and Zhaoqilin Yang
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Xin Wang: School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, China
Lingchen Kong: School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, China
Zhaoqilin Yang: Institute of Information Science, Beijing Jiaotong University, Beijing 100044, China

Mathematics, 2023, vol. 11, issue 4, 1-20

Abstract: High-dimensional covariance matrix estimation is one of the fundamental and important problems in multivariate analysis and has a wide range of applications in many fields. In practice, it is common that a covariance matrix is composed of a low-rank matrix and a sparse matrix. In this paper we estimate the covariance matrix by solving a constrained L q -type regularized optimization problem. We establish the first-order optimality conditions for this problem by using proximal mapping and the subspace method. The proposed stationary point degenerates to the first-order stationary points of the unconstrained L q regularized sparse or low-rank optimization problems. A smoothing alternating updating method is proposed to find an estimator for the covariance matrix. We establish the convergence of the proposed calculation method. The numerical simulation results show the effectiveness of the proposed approach for high-dimensional covariance estimation.

Keywords: high-dimensional covariance matrix; constrained Lq -type regularized optimization problem; smoothing alternating updating method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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