Distributional stability of sparse inverse covariance matrix estimators

• 成果类型: Article; Early Access
• 署名作者: Chen, Renjie; Xu, Huifu; Zahle, Henryk
• 署名单位: Chinese University of Hong Kong; Saarland University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610; 1436-4646
• DOI: 10.1007/s10107-026-02339-z
• 发表日期: 2026-03-09
• 关键词: covariance matrix; precision matrix; Sparse estimator; data perturbation; Distributional stability; Statistical robustness; data-driven; LOG-DETERMINANT OPTIMIZATION; qualitative robustness; STATISTICAL FUNCTIONALS; convergence-rates; model selection; Solvency II; RISK; eigenvectors; definition; inference

摘要

Finding an approximation of the inverse of the covariance matrix, also known as precision matrix, of a random vector with empirical data is widely discussed in finance and engineering. In data-driven problems, empirical data may be contaminated. This raises the question as to whether the approximate precision matrix is reliable from a statistical point of view. In this paper, we concentrate on a much-noticed sparse estimator of the precision matrix and investigate the issue from the perspective of distributional stability. Specifically, we derive an explicit local Lipschitz bound for the distance between the distributions of the sparse estimator under two different distributions (regarded as the true data distribution and the distribution of contaminated data). The distance is measured by the Kantorovich metric on the set of all probability measures on a matrix space. We also present analogous results for the standard estimators of the covariance matrix and its eigenvalues. Furthermore, we discuss several applications and conduct some numerical experiments.