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Inference on multiple correlation coefficients with moderately high dimensional data

Author

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  • Shurong Zheng
  • Dandan Jiang
  • Zhidong Bai
  • Xuming He

Abstract

When the multiple correlation coefficient is used to measure how strongly a given variable can be linearly associated with a set of covariates, it suffers from an upward bias that cannot be ignored in the presence of a moderately high dimensional covariate. Under an independent component model, we derive an asymptotic approximation to the distribution of the squared multiple correlation coefficient that depends on a simple correction factor. We show that this approximation enables us to construct reliable confidence intervals on the population coefficient even when the ratio of the dimension to the sample size is close to unity and the variables are non-Gaussian.

Suggested Citation

  • 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.
    • Handle: RePEc:oup:biomet:v:101:y:2014:i:3:p:748-754.
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    File URL: http://hdl.handle.net/10.1093/biomet/asu023
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    Cited by:

    1. Matsushita, Yukitoshi & Otsu, Taisuke, 2020. "Jackknife empirical likelihood: small bandwidth, sparse network and high-dimension asymptotic," LSE Research Online Documents on Economics 106488, London School of Economics and Political Science, LSE Library.
    2. Ding, Hao & Qin, Shanshan & Wu, Yuehua & Wu, Yaohua, 2021. "Asymptotic properties on high-dimensional multivariate regression M-estimation," Journal of Multivariate Analysis, Elsevier, vol. 183(C).
    3. Matias D. Cattaneo & Michael Jansson & Whitney K. Newey, 2018. "Inference in Linear Regression Models with Many Covariates and Heteroscedasticity," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(523), pages 1350-1361, July.
    4. Najarzadeh, Dariush, 2020. "A simple test for zero multiple correlation coefficient in high-dimensional normal data using random projection," Computational Statistics & Data Analysis, Elsevier, vol. 148(C).
    5. 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.
    6. Yukitoshi Matsushita & Taisuke Otsu, 2019. "Jackknife, small bandwidth and high-dimensional asymptotics," STICERD - Econometrics Paper Series 605, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.

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