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Partial projective resampling method for dimension reduction: With applications to partially linear models

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  • Hilafu, Haileab
  • Wu, Wenbo

Abstract

In many regression applications, the predictors naturally fall into two categories: “the predictors of primary interest” and “the predictors of secondary interest”. It is often desirable to have a dimension reduction method that focuses on the predictors of primary interest while controlling the effect of the predictors of secondary interest. To achieve this goal, a partial dimension reduction method via projective resampling of a composite vector containing the response variable(s) and the predictors of secondary interest is proposed. The proposed method is general in the sense that the predictors of secondary interest can be quantitative, categorical or a combination of both. An application of the proposed method for estimation in partially linear models is emphasized. The performance of the proposed method is assessed and compared with other competing methods via extensive simulation. The empirical results show that, in addition to the superior estimation accuracy, the proposed method has a considerable computational advantage. We also demonstrate the usefulness of the proposed method by analyzing two real datasets.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:109:y:2017:i:c:p:1-14
    DOI: 10.1016/j.csda.2016.12.002
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    References listed on IDEAS

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    1. repec:wyi:journl:002176 is not listed on IDEAS
    2. Jae Keun Yoo & R. Dennis Cook, 2007. "Optimal sufficient dimension reduction for the conditional mean in multivariate regression," Biometrika, Biometrika Trust, vol. 94(1), pages 231-242.
    3. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    4. Yu Y. & Ruppert D., 2002. "Penalized Spline Estimation for Partially Linear Single-Index Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1042-1054, December.
    5. 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.
    6. Hilafu, Haileab & Yin, Xiangrong, 2013. "Sufficient dimension reduction in multivariate regressions with categorical predictors," Computational Statistics & Data Analysis, Elsevier, vol. 63(C), pages 139-147.
    7. Li, Bing & Wen, Songqiao & Zhu, Lixing, 2008. "On a Projective Resampling Method for Dimension Reduction With Multivariate Responses," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 1177-1186.
    8. Zhenghui Feng & Xuerong Meggie Wen & Zhou Yu & Lixing Zhu, 2013. "On Partial Sufficient Dimension Reduction With Applications to Partially Linear Multi-Index Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(501), pages 237-246, March.
    9. Xia, Yingcun & Härdle, Wolfgang, 2006. "Semi-parametric estimation of partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1162-1184, May.
    10. Li, Lexin & Li, Bing & Zhu, Li-Xing, 2010. "Groupwise Dimension Reduction," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1188-1201.
    11. Lexin Li & Liping Zhu & Lixing Zhu, 2011. "Inference on the primary parameter of interest with the aid of dimension reduction estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(1), pages 59-80, January.
    12. Li, Qi, 2000. "Efficient Estimation of Additive Partially Linear Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(4), pages 1073-1092, November.
    13. Wen, Xuerong Meggie, 2007. "A note on sufficient dimension reduction," Statistics & Probability Letters, Elsevier, vol. 77(8), pages 817-821, April.
    14. Liping Zhu & Tao Wang & Lixing Zhu & Louis Ferré, 2010. "Sufficient dimension reduction through discretization-expectation estimation," Biometrika, Biometrika Trust, vol. 97(2), pages 295-304.
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