Positive-Definite l1-Penalized Estimation of Large Covariance Matrices

• 成果类型: Article
• 署名作者: Xue, Lingzhou; Ma, Shiqian; Zou, Hui
• 署名单位: Princeton University; Chinese University of Hong Kong; University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2012.725386
• 发表日期: 2012
• 页码: 1480-1491
• 关键词: 1st-order methods; SPARSE; selection; set

摘要

The thresholding covariance estimator has nice asymptotic properties for estimating sparse large covariance matrices, but it often has negative eigenvalues when used in real data analysis. To fix this drawback of thresholding estimation, we develop a positive-definite l(1)-penalized covariance estimator for estimating sparse large covariance matrices. We derive an efficient alternating direction method to solve the challenging optimization problem and establish its convergence properties. Under weak regularity conditions, nonasymptotic statistical theory is also established for the proposed estimator. The competitive finite-sample performance of our proposal is demonstrated by both simulation and real applications.