Estimation of functionals of sparse covariance matrices
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Author(s)
Fan, Jianqing
Rigollet, Philippe
Wang, Weichen
Date Issued
December 2015
Journal
Annals of Statistics
Publisher
Institute of Mathematical Statistics
Citation
Fan, Jianqing et al. “Estimation of Functionals of Sparse Covariance Matrices.” The Annals of Statistics 43, 6 (December 2015): 2706–2737 © 2015 Institute of Mathematical Statistics
Version
Final published version
Abstract
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 Lr 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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1214/15-AOS1357
