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Cross projection test for mean vectors via multiple random splits in high dimensions

Author

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  • Wang, Guanpeng
  • Wu, Jiujing
  • Cui, Hengjian

Abstract

The cross projection test (CPT) technique is extended to high-dimensional two-sample mean tests in this article, which was first proposed by Wang and Cui (2024). A data-splitting strategy is required to find the projection directions that reduce the data from high dimensional space to low dimensional space which can well solve the issue of “the curse of dimensionality”. As long as both samples are randomly split once, two correlated cross projection statistics can be established according to the CPT development mechanism, which is similar to all constructed test statistics that exist the correlation caused by multiple random splits. To deal with this issue and improve the performance of empirical powers by eliminating the randomness of data-splitting, we further utilize a powerful Cauchy combination test algorithm based on multiple data-splitting. Theoretically, we prove the asymptotic property of the proposed test statistic. Furthermore, for the sparse alternative case, we apply the power enhancement technique to the ensemble Cauchy combination test-based algorithm in marginal screening for the full data. Numerical studies through Monte Carlo simulations and two real data examples are conducted simultaneously to illustrate the utility of our proposed ensemble algorithm.

Suggested Citation

  • Wang, Guanpeng & Wu, Jiujing & Cui, Hengjian, 2024. "Cross projection test for mean vectors via multiple random splits in high dimensions," Journal of Multivariate Analysis, Elsevier, vol. 204(C).
    • Handle: RePEc:eee:jmvana:v:204:y:2024:i:c:s0047259x24000654
    DOI: 10.1016/j.jmva.2024.105358
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    References listed on IDEAS

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    1. Hyodo, Masashi & Nishiyama, Takahiro & Pavlenko, Tatjana, 2023. "A Behrens–Fisher problem for general factor models in high dimensions," Journal of Multivariate Analysis, Elsevier, vol. 195(C).
    2. Yaowu Liu & Jun Xie, 2020. "Cauchy Combination Test: A Powerful Test With Analytic p-Value Calculation Under Arbitrary Dependency Structures," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(529), pages 393-402, January.
    3. Srivastava, Muni S., 2009. "A test for the mean vector with fewer observations than the dimension under non-normality," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 518-532, March.
    4. Roger S. Zoh & Abhra Sarkar & Raymond J. Carroll & Bani K. Mallick, 2018. "A Powerful Bayesian Test for Equality of Means in High Dimensions," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(524), pages 1733-1741, October.
    5. 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.
    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. Yuanyuan Jiang & Xingzhong Xu, 2022. "A Two-Sample Test of High Dimensional Means Based on Posterior Bayes Factor," Mathematics, MDPI, vol. 10(10), pages 1-23, May.
    8. Wang, Rui & Xu, Xingzhong, 2018. "On two-sample mean tests under spiked covariances," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 225-249.
    9. Cheng, Guanghui & Liu, Baisen & Tian, Guoliang & Zheng, Shurong, 2020. "Testing proportionality of two high-dimensional covariance matrices," Computational Statistics & Data Analysis, Elsevier, vol. 150(C).
    10. 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.
    11. Changcheng Li Runze Li, 2022. "Linear Hypothesis Testing in Linear Models With High-Dimensional Responses," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(540), pages 1738-1750, October.
    12. Jianqing Fan & Yuan Liao & Jiawei Yao, 2015. "Power Enhancement in High‐Dimensional Cross‐Sectional Tests," Econometrica, Econometric Society, vol. 83(4), pages 1497-1541, July.
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