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An adaptive test for the mean vector in large-p-small-n problems

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  • Shen, Yanfeng
  • Lin, Zhengyan

Abstract

The problem of testing the mean vector in a high-dimensional setting is considered. Up to date, most high-dimensional tests for the mean vector only make use of the marginal information from the variables, and do not incorporate the correlation information into the test statistics. A new testing procedure is proposed, which makes use of the covariance information between the variables. The new approach is novel in that it can select important variables that contain evidence against the null hypothesis and reduce the impact of noise accumulation. Simulations and real data analysis demonstrate that the new test has higher power than some competing methods proposed in the literature.

Suggested Citation

  • Shen, Yanfeng & Lin, Zhengyan, 2015. "An adaptive test for the mean vector in large-p-small-n problems," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 25-38.
  • Handle: RePEc:eee:csdana:v:89:y:2015:i:c:p:25-38
    DOI: 10.1016/j.csda.2015.03.004
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    References listed on IDEAS

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    1. Ledoit, Olivier & Wolf, Michael, 2004. "A well-conditioned estimator for large-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 365-411, February.
    2. Warton, David I., 2008. "Penalized Normal Likelihood and Ridge Regularization of Correlation and Covariance Matrices," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 340-349, March.
    3. Chen, Song Xi & Li, Jun & Zhong, Pingshou, 2014. "Two-Sample Tests for High Dimensional Means with Thresholding and Data Transformation," MPRA Paper 59815, University Library of Munich, Germany.
    4. Shen, Yanfeng & Lin, Zhengyan & Zhu, Jun, 2011. "Shrinkage-based regularization tests for high-dimensional data with application to gene set analysis," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2221-2233, July.
    5. Jianqing Fan & Yang Feng & Xin Tong, 2012. "A road to classification in high dimensional space: the regularized optimal affine discriminant," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(4), pages 745-771, September.
    6. T. Tony Cai & Weidong Liu & Yin Xia, 2014. "Two-sample test of high dimensional means under dependence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(2), pages 349-372, March.
    7. Schäfer Juliane & Strimmer Korbinian, 2005. "A Shrinkage Approach to Large-Scale Covariance Matrix Estimation and Implications for Functional Genomics," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 4(1), pages 1-32, November.
    8. Cai, Tony & Liu, Weidong, 2011. "Adaptive Thresholding for Sparse Covariance Matrix Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 672-684.
    9. Srivastava, Muni S. & Du, Meng, 2008. "A test for the mean vector with fewer observations than the dimension," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 386-402, March.
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    Cited by:

    1. repec:eee:jmvana:v:167:y:2018:i:c:p:284-305 is not listed on IDEAS
    2. Zhang, Jie & Pan, Meng, 2016. "A high-dimension two-sample test for the mean using cluster subspaces," Computational Statistics & Data Analysis, Elsevier, vol. 97(C), pages 87-97.

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