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On permutation tests for predictor contribution in sufficient dimension reduction

Author

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  • Dong, Yuexiao
  • Yang, Chaozheng
  • Yu, Zhou

Abstract

To test predictor contribution in a model-free fashion, marginal coordinate tests based on sliced inverse regression (SIR) and sliced average variance estimation (SAVE) have been studied in Cook (2004), and Shao et al. (2007) respectively. Estimating the null distributions of the test statistics is a critical step for such tests. We propose a novel permutation test approach to facilitate the marginal coordinate tests, which applies to existing tests based on SIR and SAVE, and can be readily extended to a new marginal coordinate test based on directional regression (Li and Wang, 2007).

Suggested Citation

  • Dong, Yuexiao & Yang, Chaozheng & Yu, Zhou, 2016. "On permutation tests for predictor contribution in sufficient dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 149(C), pages 81-91.
    • Handle: RePEc:eee:jmvana:v:149:y:2016:i:c:p:81-91
    DOI: 10.1016/j.jmva.2016.02.019
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    References listed on IDEAS

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    1. T. Wang & X. Guo & L. Zhu & P. Xu, 2014. "Transformed sufficient dimension reduction," Biometrika, Biometrika Trust, vol. 101(4), pages 815-829.
    2. Li, Bing & Wang, Shaoli, 2007. "On Directional Regression for Dimension Reduction," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 997-1008, September.
    3. Yongwu Shao & R. Dennis Cook & Sanford Weisberg, 2007. "Marginal tests with sliced average variance estimation," Biometrika, Biometrika Trust, vol. 94(2), pages 285-296.
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