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- Publisher Website: 10.1214/15-AOS1357
- Scopus: eid_2-s2.0-84946741381
- PMID: 26806986
- WOS: WOS:000363437900014
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Article: Estimation of functionals of sparse covariance matrices
Title | Estimation of functionals of sparse covariance matrices |
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Authors | |
Keywords | Minimax Elbow effect High-dimensional testing Functional estimation Covariance matrix |
Issue Date | 2015 |
Citation | Annals of Statistics, 2015, v. 43, n. 6, p. 2706-2737 How to Cite? |
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. |
Persistent Identifier | http://hdl.handle.net/10722/303464 |
ISSN | 2023 Impact Factor: 3.2 2023 SCImago Journal Rankings: 5.335 |
PubMed Central ID | |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Fan, Jianqing | - |
dc.contributor.author | Rigollet, Philippe | - |
dc.contributor.author | Wang, Weichen | - |
dc.date.accessioned | 2021-09-15T08:25:22Z | - |
dc.date.available | 2021-09-15T08:25:22Z | - |
dc.date.issued | 2015 | - |
dc.identifier.citation | Annals of Statistics, 2015, v. 43, n. 6, p. 2706-2737 | - |
dc.identifier.issn | 0090-5364 | - |
dc.identifier.uri | http://hdl.handle.net/10722/303464 | - |
dc.description.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. | - |
dc.language | eng | - |
dc.relation.ispartof | Annals of Statistics | - |
dc.subject | Minimax | - |
dc.subject | Elbow effect | - |
dc.subject | High-dimensional testing | - |
dc.subject | Functional estimation | - |
dc.subject | Covariance matrix | - |
dc.title | Estimation of functionals of sparse covariance matrices | - |
dc.type | Article | - |
dc.description.nature | link_to_OA_fulltext | - |
dc.identifier.doi | 10.1214/15-AOS1357 | - |
dc.identifier.pmid | 26806986 | - |
dc.identifier.pmcid | PMC4719663 | - |
dc.identifier.scopus | eid_2-s2.0-84946741381 | - |
dc.identifier.volume | 43 | - |
dc.identifier.issue | 6 | - |
dc.identifier.spage | 2706 | - |
dc.identifier.epage | 2737 | - |
dc.identifier.isi | WOS:000363437900014 | - |