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Fréchet kernel sliced inverse regression

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  • Dong, Yushen
  • Wu, Yichao

Abstract

Fréchet regression is an extension of classical regression to study the relationship between a metric space-valued response and Euclidean predictors. In this paper, we propose a Fréchet kernel sliced inverse regression to perform sufficient dimension reduction for Fréchet regression and prove its consistency. Simulation examples and a real data example are used to illustrate its superb finite-sample performance.

Suggested Citation

  • Dong, Yushen & Wu, Yichao, 2022. "Fréchet kernel sliced inverse regression," Journal of Multivariate Analysis, Elsevier, vol. 191(C).
    • Handle: RePEc:eee:jmvana:v:191:y:2022:i:c:s0047259x22000495
    DOI: 10.1016/j.jmva.2022.105032
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    References listed on IDEAS

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    1. R. Dennis Cook & Xin Zhang, 2015. "Foundations for Envelope Models and Methods," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 599-611, June.
    2. Wei Luo & Bing Li, 2016. "Combining eigenvalues and variation of eigenvectors for order determination," Biometrika, Biometrika Trust, vol. 103(4), pages 875-887.
    3. Yanyuan Ma & Liping Zhu, 2013. "A Review on Dimension Reduction," International Statistical Review, International Statistical Institute, vol. 81(1), pages 134-150, April.
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    Cited by:

    1. Zhang, Qi & Li, Bing & Xue, Lingzhou, 2024. "Nonlinear sufficient dimension reduction for distribution-on-distribution regression," Journal of Multivariate Analysis, Elsevier, vol. 202(C).

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