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The hybrid method of FSIR and FSAVE for functional effective dimension reduction

Author

Listed:
  • Wang, Guochang
  • Zhou, Yan
  • Feng, Xiang-Nan
  • Zhang, Baoxue

Abstract

Functional Sliced Inverse Regression (FSIR) and Functional Sliced Average Variance Estimation (FSAVE) are two popular functional effective dimension reduction methods. However, both of them have restrictions: FSIR is vulnerable to symmetric dependencies and FSAVE has low efficiency for monotone dependencies and is sensitive to the number of slices. To avoid aforementioned disadvantages, a hybrid method of FSIR and FSAVE is developed. Theoretical properties for the hybrid method and the consistency result of the proposed hybrid estimator are derived. Simulation studies show that the hybrid method has better performance than those of FSIR and FSAVE. The proposed method is also applied on the Tecator data set.

Suggested Citation

  • Wang, Guochang & Zhou, Yan & Feng, Xiang-Nan & Zhang, Baoxue, 2015. "The hybrid method of FSIR and FSAVE for functional effective dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 91(C), pages 64-77.
    • Handle: RePEc:eee:csdana:v:91:y:2015:i:c:p:64-77
    DOI: 10.1016/j.csda.2015.05.011
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    References listed on IDEAS

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    1. Wang, Guochang & Lin, Nan & Zhang, Baoxue, 2014. "Functional k-means inverse regression," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 172-182.
    2. Amato, U. & Antoniadis, A. & De Feis, I., 2006. "Dimension reduction in functional regression with applications," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2422-2446, May.
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    4. Wang, Guochang & Lin, Nan & Zhang, Baoxue, 2013. "Functional contour regression," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 1-13.
    5. Zhu, Li-Xing & Ohtaki, Megu & Li, Yingxing, 2007. "On hybrid methods of inverse regression-based algorithms," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2621-2635, February.
    6. Lian, Heng & Li, Gaorong, 2014. "Series expansion for functional sufficient dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 150-165.
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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. Guochang Wang & Xinyuan Song, 2018. "Functional Sufficient Dimension Reduction for Functional Data Classification," Journal of Classification, Springer;The Classification Society, vol. 35(2), pages 250-272, July.
    3. Guochang Wang & Beiting Liang & Hansheng Wang & Baoxue Zhang & Baojian Xie, 2021. "Dimension reduction for functional regression with a binary response," Statistical Papers, Springer, vol. 62(1), pages 193-208, February.
    4. Guochang Wang, 2017. "Dimension reduction in functional regression with categorical predictor," Computational Statistics, Springer, vol. 32(2), pages 585-609, June.

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