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Functional envelope for model-free sufficient dimension reduction

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  • Zhang, Xin
  • Wang, Chong
  • Wu, Yichao

Abstract

In this article, we introduce the functional envelope for sufficient dimension reduction and regression with functional and longitudinal data. Functional sufficient dimension reduction methods, especially the inverse regression estimation family of methods, usually involve solving generalized eigenvalue problems and inverting the infinite-dimensional covariance operator. With the notion of functional envelope, essentially a special type of sufficient dimension reduction subspace, we develop a generic method to circumvent the difficulties in solving the generalized eigenvalue problems and inverting the covariance directly. We derive the geometric characteristics of the functional envelope and establish the asymptotic properties of related functional envelope estimators under mild conditions. The functional envelope estimators have shown promising performance in extensive simulation studies and real data analysis.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:163:y:2018:i:c:p:37-50
    DOI: 10.1016/j.jmva.2017.09.010
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    References listed on IDEAS

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    Cited by:

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    2. Minji Lee & Zhihua Su, 2020. "A Review of Envelope Models," International Statistical Review, International Statistical Institute, vol. 88(3), pages 658-676, December.
    3. Zhu, Hanbing & Zhang, Riquan & Yu, Zhou & Lian, Heng & Liu, Yanghui, 2019. "Estimation and testing for partially functional linear errors-in-variables models," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 296-314.

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