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Aggregate Kernel Inverse Regression Estimation

Author

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  • Wenjuan Li

    (School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China)

  • Wenying Wang

    (School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China)

  • Jingsi Chen

    (School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China)

  • Weidong Rao

    (School of Mathematics and Computer Science, Jiangxi Science and Technology Normal University, Nanchang 330038, China)

Abstract

Sufficient dimension reduction (SDR) is a useful tool for nonparametric regression with high-dimensional predictors. Many existing SDR methods rely on some assumptions about the distribution of predictors. Wang et al. proposed an aggregate dimension reduction method to reduce the dependence on the distributional assumptions. Motivated by their work, we propose a novel and effective method by combining the aggregate method and the kernel inverse regression estimation. The proposed approach can accurately estimate the dimension reduction directions and substantially improve the exhaustivity of the estimates with complex models. At the same time, this method does not depend on the arrangement of slices, and the influence of the extreme values of the response is reduced. In numerical examples and a real data application, it performs well.

Suggested Citation

  • Wenjuan Li & Wenying Wang & Jingsi Chen & Weidong Rao, 2023. "Aggregate Kernel Inverse Regression Estimation," Mathematics, MDPI, vol. 11(12), pages 1-10, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2682-:d:1170250
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    References listed on IDEAS

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    1. Yanyuan Ma & Liping Zhu, 2012. "A Semiparametric Approach to Dimension Reduction," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 168-179, March.
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    10. Yang, Baoying & Yin, Xiangrong & Zhang, Nan, 2019. "Sufficient variable selection using independence measures for continuous response," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 480-493.
    11. Yuexiao Dong & Bing Li, 2010. "Dimension reduction for non-elliptically distributed predictors: second-order methods," Biometrika, Biometrika Trust, vol. 97(2), pages 279-294.
    12. Zhu, Li-Ping & Zhu, Li-Xing & Feng, Zheng-Hui, 2010. "Dimension Reduction in Regressions Through Cumulative Slicing Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1455-1466.
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