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On Partial Sufficient Dimension Reduction With Applications to Partially Linear Multi-Index Models

Author

Listed:
  • Zhenghui Feng
  • Xuerong Meggie Wen
  • Zhou Yu
  • Lixing Zhu

Abstract

Partial dimension reduction is a general method to seek informative convex combinations of predictors of primary interest, which includes dimension reduction as its special case when the predictors in the remaining part are constants. In this article, we propose a novel method to conduct partial dimension reduction estimation for predictors of primary interest without assuming that the remaining predictors are categorical. To this end, we first take the dichotomization step such that any existing approach for partial dimension reduction estimation can be employed. Then we take the expectation step to integrate over all the dichotomic predictors to identify the partial central subspace. As an example, we use the partially linear multi-index model to illustrate its applications for semiparametric modeling. Simulations and real data examples are given to illustrate our methodology.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:jnlasa:v:108:y:2013:i:501:p:237-246
    DOI: 10.1080/01621459.2012.746065
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    References listed on IDEAS

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    1. 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.
    2. Zhu, Lixing & Miao, Baiqi & Peng, Heng, 2006. "On Sliced Inverse Regression With High-Dimensional Covariates," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 630-643, June.
    3. 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.
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    Cited by:

    1. Lu Li & Kai Tan & Xuerong Meggie Wen & Zhou Yu, 2023. "Variable-dependent partial dimension reduction," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(2), pages 521-541, June.
    2. Jun Zhang & Zhenghui Feng & Xiaoguang Wang, 2018. "A constructive hypothesis test for the single-index models with two groups," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(5), pages 1077-1114, October.
    3. Zeng, Bilin & Yu, Zhou & Wen, Xuerong Meggie, 2015. "A note on cumulative mean estimation," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 322-327.
    4. Xiaobing Zhao & Xian Zhou, 2020. "Partial sufficient dimension reduction on additive rates model for recurrent event data with high-dimensional covariates," Statistical Papers, Springer, vol. 61(2), pages 523-541, April.
    5. Ming-Yueh Huang & Kwun Chuen Gary Chan, 2022. "Model selection among Dimension-Reduced generalized Cox models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 28(3), pages 492-511, July.
    6. Ke, Chenlu & Yang, Wei & Yuan, Qingcong & Li, Lu, 2023. "Partial sufficient variable screening with categorical controls," Computational Statistics & Data Analysis, Elsevier, vol. 187(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.
    8. Lu Li & Niwen Zhou & Lixing Zhu, 2022. "Outcome regression-based estimation of conditional average treatment effect," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(5), pages 987-1041, October.

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