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August 2013 Tests for covariance matrix with fixed or divergent dimension
Rongmao Zhang, Liang Peng, Ruodu Wang
Ann. Statist. 41(4): 2075-2096 (August 2013). DOI: 10.1214/13-AOS1136


Testing covariance structure is of importance in many areas of statistical analysis, such as microarray analysis and signal processing. Conventional tests for finite-dimensional covariance cannot be applied to high-dimensional data in general, and tests for high-dimensional covariance in the literature usually depend on some special structure of the matrix. In this paper, we propose some empirical likelihood ratio tests for testing whether a covariance matrix equals a given one or has a banded structure. The asymptotic distributions of the new tests are independent of the dimension.


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Rongmao Zhang. Liang Peng. Ruodu Wang. "Tests for covariance matrix with fixed or divergent dimension." Ann. Statist. 41 (4) 2075 - 2096, August 2013.


Published: August 2013
First available in Project Euclid: 23 October 2013

zbMATH: 1277.62151
MathSciNet: MR3127858
Digital Object Identifier: 10.1214/13-AOS1136

Primary: 62F03
Secondary: 62F40

Keywords: $\chi^{2}$-distribution , Covariance matrix , empirical likelihood tests , High-dimensional data

Rights: Copyright © 2013 Institute of Mathematical Statistics


Vol.41 • No. 4 • August 2013
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