Document Type

Journal Article

Department/Unit

Department of Mathematics

Language

English

Abstract

Estimation of variances and covariances is required for many statistical methods such as t-test, principal component analysis and linear discriminant analysis. High-dimensional data such as gene expression microarray data and financial data pose challenges to traditional statistical and computational methods. In this paper, we review some recent developments in the estimation of variances, covariance matrix, and precision matrix, with emphasis on the applications to microarray data analysis.

Keywords

Covariance matrix, High-dimensional data, Microarray data, Precision matrix, Shrinkage estimation, Sparse covariance matrix

Publication Date

8-2014

Source Publication Title

Wiley Interdisciplinary Reviews: Computational Statistics

Volume

6

Issue

4

Start Page

255

End Page

264

Publisher

Wiley

Peer Reviewed

1

Copyright

This is the peer reviewed version of the following article: Tong, T., Wang, C. and Wang, Y. (2014), Estimation of variances and covariances for high-dimensional data: a selective review. WIREs Comp Stat, 6: 255–264. doi: 10.1002/wics.1308, which has been published in final form at http://dx.doi.org/10.1002/wics.1308. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.

Funder

Tiejun Tong's research was supported in part by Hong Kong Research Grant HKBU202711 and Hong Kong Baptist University FRG Grants FRG2/11-12/110 and FRGl/13-14/018. Cheng Wang's research was supported by NSF of China Grants 11101397, 71001095, and 11271347. Yuedong Wang's research was supported by NSF Grant DMS-07-06886. The authors thank the editor, the associate editor, and two referees for their constructive comments that led to a substantial improvement of this review article.

DOI

10.1002/wics.1308

Link to Publisher's Edition

http://dx.doi.org/10.1002/wics.1308

ISSN (print)

19395108

ISSN (electronic)

19390068

Included in

Mathematics Commons

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