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- Publisher Website: 10.1214/16-AOS1487
- Scopus: eid_2-s2.0-85020654111
- PMID: 28835726
- WOS: WOS:000404395900014
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Article: Asymptotics of empirical eigenstructure for high dimensional spiked covariance
Title | Asymptotics of empirical eigenstructure for high dimensional spiked covariance |
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Authors | |
Keywords | Approximate factor model Principal component analysis Relative risk management Diverging eigenvalues False discovery proportion Asymptotic distributions |
Issue Date | 2017 |
Citation | Annals of Statistics, 2017, v. 45, n. 3, p. 1342-1374 How to Cite? |
Abstract | We derive the asymptotic distributions of the spiked eigenvalues and eigenvectors under a generalized and unified asymptotic regime, which takes into account the magnitude of spiked eigenvalues, sample size and dimensionality. This regime allows high dimensionality and diverging eigenvalues and provides new insights into the roles that the leading eigenvalues, sample size and dimensionality play in principal component analysis. Our results are a natural extension of those in [Statist. Sinica 17 (2007) 1617-1642] to a more general setting and solve the rates of convergence problems in [Statist. Sinica 26 (2016) 1747-1770]. They also reveal the biases of estimating leading eigenvalues and eigenvectors by using principal component analysis, and lead to a new covariance estimator for the approximate factor model, called Shrinkage Principal Orthogonal complEment Thresholding (S-POET), that corrects the biases. Our results are successfully applied to outstanding problems in estimation of risks for large portfolios and false discovery proportions for dependent test statistics and are illustrated by simulation studies. |
Persistent Identifier | http://hdl.handle.net/10722/303527 |
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 | Wang, Weichen | - |
dc.contributor.author | Fan, Jianqing | - |
dc.date.accessioned | 2021-09-15T08:25:30Z | - |
dc.date.available | 2021-09-15T08:25:30Z | - |
dc.date.issued | 2017 | - |
dc.identifier.citation | Annals of Statistics, 2017, v. 45, n. 3, p. 1342-1374 | - |
dc.identifier.issn | 0090-5364 | - |
dc.identifier.uri | http://hdl.handle.net/10722/303527 | - |
dc.description.abstract | We derive the asymptotic distributions of the spiked eigenvalues and eigenvectors under a generalized and unified asymptotic regime, which takes into account the magnitude of spiked eigenvalues, sample size and dimensionality. This regime allows high dimensionality and diverging eigenvalues and provides new insights into the roles that the leading eigenvalues, sample size and dimensionality play in principal component analysis. Our results are a natural extension of those in [Statist. Sinica 17 (2007) 1617-1642] to a more general setting and solve the rates of convergence problems in [Statist. Sinica 26 (2016) 1747-1770]. They also reveal the biases of estimating leading eigenvalues and eigenvectors by using principal component analysis, and lead to a new covariance estimator for the approximate factor model, called Shrinkage Principal Orthogonal complEment Thresholding (S-POET), that corrects the biases. Our results are successfully applied to outstanding problems in estimation of risks for large portfolios and false discovery proportions for dependent test statistics and are illustrated by simulation studies. | - |
dc.language | eng | - |
dc.relation.ispartof | Annals of Statistics | - |
dc.subject | Approximate factor model | - |
dc.subject | Principal component analysis | - |
dc.subject | Relative risk management | - |
dc.subject | Diverging eigenvalues | - |
dc.subject | False discovery proportion | - |
dc.subject | Asymptotic distributions | - |
dc.title | Asymptotics of empirical eigenstructure for high dimensional spiked covariance | - |
dc.type | Article | - |
dc.description.nature | link_to_OA_fulltext | - |
dc.identifier.doi | 10.1214/16-AOS1487 | - |
dc.identifier.pmid | 28835726 | - |
dc.identifier.pmcid | PMC5563862 | - |
dc.identifier.scopus | eid_2-s2.0-85020654111 | - |
dc.identifier.volume | 45 | - |
dc.identifier.issue | 3 | - |
dc.identifier.spage | 1342 | - |
dc.identifier.epage | 1374 | - |
dc.identifier.isi | WOS:000404395900014 | - |