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High-dimensional regression analysis with treatment comparisons

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  • Heng-Hui Lue
  • Bing-Ran You

Abstract

We consider the treatment comparison problem in a general high-dimensional regression setting. In this article, we propose a nonparametric estimation approach based on partial sliced inverse regression (SIR) (Chiaromonte et al. in Ann Stat 30:475–497, 2002 ) and an extension of partial inverse mean matching (Carroll and Li in Stat Sin 5:667–688, 1995 ) without requiring a prespecified parametric model. A sparse estimation strategy is incorporated in our approach to enhance the interpretation of variable selection. Several simulation examples are used to compare our method with SIR and principal components analysis. Illustrative applications to two real datasets are also presented. Copyright Springer-Verlag 2013

Suggested Citation

  • Heng-Hui Lue & Bing-Ran You, 2013. "High-dimensional regression analysis with treatment comparisons," Computational Statistics, Springer, vol. 28(3), pages 1299-1317, June.
    • Handle: RePEc:spr:compst:v:28:y:2013:i:3:p:1299-1317
    DOI: 10.1007/s00180-012-0357-6
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    References listed on IDEAS

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    1. Liqiang Ni & R. Dennis Cook & Chih-Ling Tsai, 2005. "A note on shrinkage sliced inverse regression," Biometrika, Biometrika Trust, vol. 92(1), pages 242-247, March.
    2. Yingcun Xia & Howell Tong & W. K. Li & Li‐Xing Zhu, 2002. "An adaptive estimation of dimension reduction space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 363-410, August.
    3. Lexin Li & R. Dennis Cook & Christopher J. Nachtsheim, 2005. "Model‐free variable selection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 285-299, April.
    4. Lexin Li, 2007. "Sparse sufficient dimension reduction," Biometrika, Biometrika Trust, vol. 94(3), pages 603-613.
    5. Zhu, Yu & Zeng, Peng, 2006. "Fourier Methods for Estimating the Central Subspace and the Central Mean Subspace in Regression," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1638-1651, December.
    6. Efstathia Bura & R. Dennis Cook, 2001. "Estimating the structural dimension of regressions via parametric inverse regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 393-410.
    7. Eaton, Morris L., 1986. "A characterization of spherical distributions," Journal of Multivariate Analysis, Elsevier, vol. 20(2), pages 272-276, December.
    8. Cook, R. Dennis & Ni, Liqiang, 2005. "Sufficient Dimension Reduction via Inverse Regression: A Minimum Discrepancy Approach," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 410-428, June.
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