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Testing the order of a population spectral distribution for high-dimensional data

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  • Qin, Yingli
  • Li, Weiming

Abstract

Large covariance matrices play a fundamental role in various high-dimensional statistics. Investigating the limiting behavior of the eigenvalues can reveal informative structures of large covariance matrices, which is particularly important in high-dimensional principal component analysis and covariance matrix estimation. In this paper, we propose a framework to test the number of distinct population eigenvalues for large covariance matrices, i.e. the order of a Population Spectral Distribution. The limiting distribution of our test statistic for a Population Spectral Distribution of order 2 is developed along with its (N,p) consistency, which is clearly demonstrated in our simulation study. We also apply our test to two classical microarray datasets.

Suggested Citation

  • Qin, Yingli & Li, Weiming, 2016. "Testing the order of a population spectral distribution for high-dimensional data," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 75-82.
    • Handle: RePEc:eee:csdana:v:95:y:2016:i:c:p:75-82
    DOI: 10.1016/j.csda.2015.09.009
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    References listed on IDEAS

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    1. Weiming Li & Jianfeng Yao, 2015. "On generalized expectation-based estimation of a population spectral distribution from high-dimensional data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(2), pages 359-373, April.
    2. Srivastava, Muni S. & Kollo, Tõnu & von Rosen, Dietrich, 2011. "Some tests for the covariance matrix with fewer observations than the dimension under non-normality," Journal of Multivariate Analysis, Elsevier, vol. 102(6), pages 1090-1103, July.
    3. Fisher, Thomas J. & Sun, Xiaoqian & Gallagher, Colin M., 2010. "A new test for sphericity of the covariance matrix for high dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2554-2570, November.
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