ESTIMATION OF FUNCTIONALS OF SPARSE COVARIANCE MATRICES

• 成果类型: Article
• 署名作者: Fan, Jianqing; Rigollet, Philippe; Wang, Weichen
• 署名单位: Princeton University; Massachusetts Institute of Technology (MIT)
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/15-AOS1357
• 发表日期: 2015
• 页码: 2706-2737
• 关键词: optimal adaptive estimation; Optimal Rates; principal-components; high dimension; CONVERGENCE; PCA; equilibrium; Consistency; sharp

摘要

High-dimensional statistical tests often ignore correlations to gain simplicity and stability leading to null distributions that depend on functionals of correlation matrices such as their Frobenius norm and other l(r) norms. Motivated by the computation of critical values of such tests, we investigate the difficulty of estimation the functionals of sparse correlation matrices. Specifically, we show that simple plug-in procedures based on thresholded estimators of correlation matrices are sparsity-adaptive and minimax optimal over a large class of correlation matrices. Akin to previous results on functional estimation, the minimax rates exhibit an elbow phenomenon. Our results are further illustrated in simulated data as well as an empirical study of data arising in financial econometrics.