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Fused Estimators of the Central Subspace in Sufficient Dimension Reduction

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  • R. Dennis Cook
  • Xin Zhang

Abstract

When studying the regression of a univariate variable Y on a vector x of predictors, most existing sufficient dimension-reduction (SDR) methods require the construction of slices of Y to estimate moments of the conditional distribution of X given Y . But there is no widely accepted method for choosing the number of slices, while a poorly chosen slicing scheme may produce miserable results. We propose a novel and easily implemented fusing method that can mitigate the problem of choosing a slicing scheme and improve estimation efficiency at the same time. We develop two fused estimators-called FIRE and DIRE-based on an optimal inverse regression estimator. The asymptotic variance of FIRE is no larger than that of the original methods regardless of the choice of slicing scheme, while DIRE is less computational intense and more robust. Simulation studies show that the fused estimators perform effectively the same as or substantially better than the parent methods. Fused estimators based on other methods can be developed in parallel: fused sliced inverse regression (SIR), fused central solution space (CSS)-SIR, and fused likelihood-based method (LAD) are introduced briefly. Simulation studies of the fused CSS-SIR and fused LAD estimators show substantial gain over their parent methods. A real data example is also presented for illustration and comparison. Supplementary materials for this article are available online.

Suggested Citation

  • R. Dennis Cook & Xin Zhang, 2014. "Fused Estimators of the Central Subspace in Sufficient Dimension Reduction," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 815-827, June.
  • Handle: RePEc:taf:jnlasa:v:109:y:2014:i:506:p:815-827
    DOI: 10.1080/01621459.2013.866563
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    Citations

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    Cited by:

    1. Zhang, Xin & Wang, Chong & Wu, Yichao, 2018. "Functional envelope for model-free sufficient dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 163(C), pages 37-50.
    2. Liu, Yanyan & Zhang, Jing & Zhao, Xingqiu, 2018. "A new nonparametric screening method for ultrahigh-dimensional survival data," Computational Statistics & Data Analysis, Elsevier, vol. 119(C), pages 74-85.
    3. Ming-Yueh Huang & Chin-Tsang Chiang, 2017. "An Effective Semiparametric Estimation Approach for the Sufficient Dimension Reduction Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1296-1310, July.
    4. Xue, Yuan & Yin, Xiangrong & Jiang, Xiaolin, 2016. "Ensemble sufficient dimension folding methods for analyzing matrix-valued data," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 193-205.
    5. Yan, Xiaodong & Tang, Niansheng & Xie, Jinhan & Ding, Xianwen & Wang, Zhiqiang, 2018. "Fused mean–variance filter for feature screening," Computational Statistics & Data Analysis, Elsevier, vol. 122(C), pages 18-32.
    6. Weng, Jiaying, 2022. "Fourier transform sparse inverse regression estimators for sufficient variable selection," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    7. Hilafu, Haileab & Wu, Wenbo, 2017. "Partial projective resampling method for dimension reduction: With applications to partially linear models," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 1-14.

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