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Sure screening by ranking the canonical correlations

Author

Listed:
  • Xin-Bing Kong

    (CASER, Soochow University)

  • Zhi Liu

    (University of Macau and UM Zhuhai Research Institute)

  • Yuan Yao

    (Hong Kong Baptist University)

  • Wang Zhou

    (National University of Singapore)

Abstract

The sure independence screening procedure by ranking the marginal Pearson correlation is well documented in literatures and works satisfactorily in the ultra-high dimensional case. However, this marginal Person correlation learning would easily miss the variable that is marginally uncorrelated with the response but correlated with the response jointly with some other variables. This failure in missing an important variable is due to the fact that the marginal Pearson correlation does not use the joint information of the response and a set of covariates. In this paper, we introduce a new screening method which leaves a variable into the active set if it jointly with some other variables has a high canonical correlation with the response. This is accomplished via ranking canonical correlations between the response and all possible sets of k variables. Our results show that the procedure has the sure screening property and substantially reduces the dimensionality to a moderate size against the sample size. Extensive simulations demonstrate that our new method performs substantially better than the existing sure independence screening approaches based on the marginal Pearson correlation or Kental’s tau rank correlation. A real data set is also analyzed by implementing our approach.

Suggested Citation

  • Xin-Bing Kong & Zhi Liu & Yuan Yao & Wang Zhou, 2017. "Sure screening by ranking the canonical correlations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 46-70, March.
    • Handle: RePEc:spr:testjl:v:26:y:2017:i:1:d:10.1007_s11749-016-0497-z
    DOI: 10.1007/s11749-016-0497-z
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    References listed on IDEAS

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    1. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    2. Zhao, Sihai Dave & Li, Yi, 2012. "Principled sure independence screening for Cox models with ultra-high-dimensional covariates," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 397-411.
    3. Fan, Jianqing & Feng, Yang & Song, Rui, 2011. "Nonparametric Independence Screening in Sparse Ultra-High-Dimensional Additive Models," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 544-557.
    4. Hengjian Cui & Runze Li & Wei Zhong, 2015. "Model-Free Feature Screening for Ultrahigh Dimensional Discriminant Analysis," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 630-641, June.
    5. 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.
    6. Jianqing Fan & Yunbei Ma & Wei Dai, 2014. "Nonparametric Independence Screening in Sparse Ultra-High-Dimensional Varying Coefficient Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1270-1284, September.
    7. Jianqing Fan & Jinchi Lv, 2008. "Sure independence screening for ultrahigh dimensional feature space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 849-911, November.
    8. Peter Hall & D. M. Titterington & Jing‐Hao Xue, 2009. "Tilting methods for assessing the influence of components in a classifier," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(4), pages 783-803, September.
    9. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
    10. Antoniadis A. & Fan J., 2001. "Regularization of Wavelet Approximations," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 939-967, September.
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