A Comparison of Methods for Estimating the Determinant of High-Dimensional Covariance Matrix

Handle URI:
http://hdl.handle.net/10754/626391
Title:
A Comparison of Methods for Estimating the Determinant of High-Dimensional Covariance Matrix
Authors:
Hu, Zongliang; Dong, Kai; Dai, Wenlin; Tong, Tiejun
Abstract:
The determinant of the covariance matrix for high-dimensional data plays an important role in statistical inference and decision. It has many real applications including statistical tests and information theory. Due to the statistical and computational challenges with high dimensionality, little work has been proposed in the literature for estimating the determinant of high-dimensional covariance matrix. In this paper, we estimate the determinant of the covariance matrix using some recent proposals for estimating high-dimensional covariance matrix. Specifically, we consider a total of eight covariance matrix estimation methods for comparison. Through extensive simulation studies, we explore and summarize some interesting comparison results among all compared methods. We also provide practical guidelines based on the sample size, the dimension, and the correlation of the data set for estimating the determinant of high-dimensional covariance matrix. Finally, from a perspective of the loss function, the comparison study in this paper may also serve as a proxy to assess the performance of the covariance matrix estimation.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Hu Z, Dong K, Dai W, Tong T (2017) A Comparison of Methods for Estimating the Determinant of High-Dimensional Covariance Matrix. The International Journal of Biostatistics 13. Available: http://dx.doi.org/10.1515/ijb-2017-0013.
Publisher:
Walter de Gruyter GmbH
Journal:
The International Journal of Biostatistics
Issue Date:
27-Sep-2017
DOI:
10.1515/ijb-2017-0013
Type:
Article
ISSN:
1557-4679
Sponsors:
Supported by the National Natural Science Foundation of China grant (No. 11671338), and the Hong Kong Baptist University grants FRG2/15-16/019, FRG2/15-16/038 and FRG1/16-17/018.
Additional Links:
https://www.degruyter.com/view/j/ijb.2017.13.issue-2/ijb-2017-0013/ijb-2017-0013.xml
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorHu, Zongliangen
dc.contributor.authorDong, Kaien
dc.contributor.authorDai, Wenlinen
dc.contributor.authorTong, Tiejunen
dc.date.accessioned2017-12-18T13:52:33Z-
dc.date.available2017-12-18T13:52:33Z-
dc.date.issued2017-09-27en
dc.identifier.citationHu Z, Dong K, Dai W, Tong T (2017) A Comparison of Methods for Estimating the Determinant of High-Dimensional Covariance Matrix. The International Journal of Biostatistics 13. Available: http://dx.doi.org/10.1515/ijb-2017-0013.en
dc.identifier.issn1557-4679en
dc.identifier.doi10.1515/ijb-2017-0013en
dc.identifier.urihttp://hdl.handle.net/10754/626391-
dc.description.abstractThe determinant of the covariance matrix for high-dimensional data plays an important role in statistical inference and decision. It has many real applications including statistical tests and information theory. Due to the statistical and computational challenges with high dimensionality, little work has been proposed in the literature for estimating the determinant of high-dimensional covariance matrix. In this paper, we estimate the determinant of the covariance matrix using some recent proposals for estimating high-dimensional covariance matrix. Specifically, we consider a total of eight covariance matrix estimation methods for comparison. Through extensive simulation studies, we explore and summarize some interesting comparison results among all compared methods. We also provide practical guidelines based on the sample size, the dimension, and the correlation of the data set for estimating the determinant of high-dimensional covariance matrix. Finally, from a perspective of the loss function, the comparison study in this paper may also serve as a proxy to assess the performance of the covariance matrix estimation.en
dc.description.sponsorshipSupported by the National Natural Science Foundation of China grant (No. 11671338), and the Hong Kong Baptist University grants FRG2/15-16/019, FRG2/15-16/038 and FRG1/16-17/018.en
dc.publisherWalter de Gruyter GmbHen
dc.relation.urlhttps://www.degruyter.com/view/j/ijb.2017.13.issue-2/ijb-2017-0013/ijb-2017-0013.xmlen
dc.rightsArchived with thanks to International Journal of Biostatisticsen
dc.subjectcovariance matrixen
dc.subjecthigh-dimensional dataen
dc.subjectlog-determinant,sparse matrixen
dc.subjectshrinkage estimationen
dc.subjectthresholding estimationen
dc.titleA Comparison of Methods for Estimating the Determinant of High-Dimensional Covariance Matrixen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalThe International Journal of Biostatisticsen
dc.eprint.versionPost-printen
dc.contributor.institutionDepartment of Mathematics, Hong Kong Baptist University, Kowloon Tong, , Hong Kongen
kaust.authorTong, Tiejunen
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