Weighted Statistic in Detecting Faint and Sparse Alternatives for High-Dimensional Covariance Matrices

Weighted Statistic in Detecting Faint and Sparse Alternatives for High-Dimensional Covariance Matrices

This article considers testing equality of two population covariance matrices when the data dimension p diverges with the sample size n (p/n → c > 0). We propose a weighted test statistic that is data-driven and powerful in both faint alternatives (many small disturbances) and sparse alternatives...

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Main Authors: Yang, Qing, Pan, Guangming
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2017
Subjects:
Empirical spectral distribution
Faint alternative
Online Access:https://hdl.handle.net/10356/85597
http://hdl.handle.net/10220/43760
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-855972023-02-28T19:33:06Z Weighted Statistic in Detecting Faint and Sparse Alternatives for High-Dimensional Covariance Matrices Yang, Qing Pan, Guangming School of Physical and Mathematical Sciences Empirical spectral distribution Faint alternative This article considers testing equality of two population covariance matrices when the data dimension p diverges with the sample size n (p/n → c > 0). We propose a weighted test statistic that is data-driven and powerful in both faint alternatives (many small disturbances) and sparse alternatives (several large disturbances). Its asymptotic null distribution is derived by large random matrix theory without assuming the existence of a limiting cumulative distribution function of the population covariance matrix. The simulation results confirm that our statistic is powerful against all alternatives, while other tests given in the literature fail in at least one situation. Supplementary materials for this article are available online. MOE (Min. of Education, S’pore) Accepted version 2017-09-18T05:28:35Z 2019-12-06T16:06:51Z 2017-09-18T05:28:35Z 2019-12-06T16:06:51Z 2017 Journal Article Yang, Q., & Pan, G. (2017). Weighted Statistic in Detecting Faint and Sparse Alternatives for High-Dimensional Covariance Matrices. Journal of the American Statistical Association, 112(517), 188-200. 0162-1459 https://hdl.handle.net/10356/85597 http://hdl.handle.net/10220/43760 10.1080/01621459.2015.1122602 en Journal of the American Statistical Association © 2017 American Statistical Association. This is the author created version of a work that has been peer reviewed and accepted for publication in Journal of the American Statistical Association, published by Taylor & Francis on behalf of American Statistical Association. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [http://dx.doi.org/10.1080/01621459.2015.1122602]. 30 p. application/pdf
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic Empirical spectral distribution
Faint alternative
spellingShingle Empirical spectral distribution
Faint alternative
Yang, Qing
Pan, Guangming
Weighted Statistic in Detecting Faint and Sparse Alternatives for High-Dimensional Covariance Matrices
description This article considers testing equality of two population covariance matrices when the data dimension p diverges with the sample size n (p/n → c > 0). We propose a weighted test statistic that is data-driven and powerful in both faint alternatives (many small disturbances) and sparse alternatives (several large disturbances). Its asymptotic null distribution is derived by large random matrix theory without assuming the existence of a limiting cumulative distribution function of the population covariance matrix. The simulation results confirm that our statistic is powerful against all alternatives, while other tests given in the literature fail in at least one situation. Supplementary materials for this article are available online.
author2 School of Physical and Mathematical Sciences
author_facet School of Physical and Mathematical Sciences
Yang, Qing
Pan, Guangming
format Article
author Yang, Qing
Pan, Guangming
author_sort Yang, Qing
title Weighted Statistic in Detecting Faint and Sparse Alternatives for High-Dimensional Covariance Matrices
title_short Weighted Statistic in Detecting Faint and Sparse Alternatives for High-Dimensional Covariance Matrices
title_full Weighted Statistic in Detecting Faint and Sparse Alternatives for High-Dimensional Covariance Matrices
title_fullStr Weighted Statistic in Detecting Faint and Sparse Alternatives for High-Dimensional Covariance Matrices
title_full_unstemmed Weighted Statistic in Detecting Faint and Sparse Alternatives for High-Dimensional Covariance Matrices
title_sort weighted statistic in detecting faint and sparse alternatives for high-dimensional covariance matrices
publishDate 2017
url https://hdl.handle.net/10356/85597
http://hdl.handle.net/10220/43760
_version_ 1759855796444725248

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