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Nonparametric conditional mean testing via an extreme‐type statistic in high dimension

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  • Yiming Liu
  • Guangming Pan
  • Guangren Yang
  • Wang Zhou

Abstract

We propose a new test to investigate the conditional mean dependence between a response variable and the corresponding covariates in the high‐dimensional regimes. The test statistic is an extreme‐type one built on the nonparametric method. The limiting null distribution of the proposed extreme type statistic under a mild mixing condition is established. Moreover, to make the test more powerful in general structures we propose a more general test statistic and develop its asymptotic properties. The power analysis of both methods is also considered. In real data analysis, we also propose a new way to conduct the feature screening based on our results. To evaluate the performance of our estimators and other methods, extensive simulations are conducted.

Suggested Citation

  • Yiming Liu & Guangming Pan & Guangren Yang & Wang Zhou, 2024. "Nonparametric conditional mean testing via an extreme‐type statistic in high dimension," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 51(2), pages 801-831, June.
    • Handle: RePEc:bla:scjsta:v:51:y:2024:i:2:p:801-831
    DOI: 10.1111/sjos.12697
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    References listed on IDEAS

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    1. Runze Li & Wei Zhong & Liping Zhu, 2012. "Feature Screening via Distance Correlation Learning," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 1129-1139, September.
    2. Liu, Zhi & Xia, Xiaochao & Zhou, Wang, 2015. "A test for equality of two distributions via jackknife empirical likelihood and characteristic functions," Computational Statistics & Data Analysis, Elsevier, vol. 92(C), pages 97-114.
    3. Qing Yang & Guangming Pan, 2017. "Weighted Statistic in Detecting Faint and Sparse Alternatives for High-Dimensional Covariance Matrices," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 188-200, January.
    4. Ian W. McKeague & Min Qian, 2015. "An Adaptive Resampling Test for Detecting the Presence of Significant Predictors," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1422-1433, December.
    5. Tony Cai & Weidong Liu & Yin Xia, 2013. "Two-Sample Covariance Matrix Testing and Support Recovery in High-Dimensional and Sparse Settings," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(501), pages 265-277, March.
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