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More powerful tests for sparse high-dimensional covariances matrices

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  • Peng, Liuhua
  • Chen, Song Xi
  • Zhou, Wen

Abstract

This paper considers improving the power of tests for the identity and sphericity hypotheses regarding high dimensional covariance matrices. The power improvement is achieved by employing the banding estimator for the covariance matrices, which leads to significant reduction in the variance of the test statistics in high dimension. Theoretical justification and simulation experiments are provided to ensure the validity of the proposed tests. The tests are used to analyze a dataset from an acute lymphoblastic leukemia gene expression study for an illustration.

Suggested Citation

  • Peng, Liuhua & Chen, Song Xi & Zhou, Wen, 2016. "More powerful tests for sparse high-dimensional covariances matrices," Journal of Multivariate Analysis, Elsevier, vol. 149(C), pages 124-143.
    • Handle: RePEc:eee:jmvana:v:149:y:2016:i:c:p:124-143
    DOI: 10.1016/j.jmva.2016.03.008
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    1. Muni S. Srivastava & Hirokazu Yanagihara & Tatsuya Kubokawa, 2014. "Tests for Covariance Matrices in High Dimension with Less Sample Size," CIRJE F-Series CIRJE-F-933, CIRJE, Faculty of Economics, University of Tokyo.
    2. Anestis Touloumis & Simon Tavaré & John C. Marioni, 2015. "Testing the mean matrix in high-dimensional transposable data," Biometrics, The International Biometric Society, vol. 71(1), pages 157-166, March.
    3. Yumou Qiu & Song Xi Chen, 2015. "Bandwidth Selection for High-Dimensional Covariance Matrix Estimation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1160-1174, September.
    4. Chen, Song Xi & Zhang, Li-Xin & Zhong, Ping-Shou, 2010. "Tests for High-Dimensional Covariance Matrices," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 810-819.
    5. Friendly M., 2002. "Corrgrams: Exploratory Displays for Correlation Matrices," The American Statistician, American Statistical Association, vol. 56, pages 316-324, November.
    6. Srivastava, Muni S. & Reid, N., 2012. "Testing the structure of the covariance matrix with fewer observations than the dimension," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 156-171.
    7. Bai, Z. D. & Silverstein, Jack W. & Yin, Y. Q., 1988. "A note on the largest eigenvalue of a large dimensional sample covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 26(2), pages 166-168, August.
    8. James R. Schott, 2005. "Testing for complete independence in high dimensions," Biometrika, Biometrika Trust, vol. 92(4), pages 951-956, December.
    9. Changliang Zou & Liuhua Peng & Long Feng & Zhaojun Wang, 2014. "Multivariate sign-based high-dimensional tests for sphericity," Biometrika, Biometrika Trust, vol. 101(1), pages 229-236.
    10. Rothman, Adam J. & Levina, Elizaveta & Zhu, Ji, 2009. "Generalized Thresholding of Large Covariance Matrices," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 177-186.
    11. Srivastava, Muni S. & Yanagihara, Hirokazu, 2010. "Testing the equality of several covariance matrices with fewer observations than the dimension," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1319-1329, July.
    12. Chen, Song Xi & Qin, Yingli, 2010. "A Two Sample Test for High Dimensional Data with Applications to Gene-set Testing," MPRA Paper 59642, University Library of Munich, Germany.
    13. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    14. Shurong Zheng & Dandan Jiang & Zhidong Bai & Xuming He, 2014. "Inference on multiple correlation coefficients with moderately high dimensional data," Biometrika, Biometrika Trust, vol. 101(3), pages 748-754.
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    Cited by:

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    2. Zhendong Wang & Xingzhong Xu, 2021. "High-dimensional sphericity test by extended likelihood ratio," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(8), pages 1169-1212, November.

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