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Functional envelope for model-free sufficient dimension reduction

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journal contribution
posted on 19.06.2018, 00:00 by Xin Zhang, Chong Wang, Yichao Wu
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.

Funding

Wu is supported by NSF grant DMS–1055210. Zhang is supported by NSF grant DMS–1613154 and CCF-1617691.

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Citation

Zhang, X., Wang, C. and Wu, Y. C. Functional envelope for model-free sufficient dimension reduction. Journal of Multivariate Analysis. 2018. 163: 37-50. 10.1016/j.jmva.2017.09.010

Publisher

Elsevier

Language

en_US

issn

0047-259X

Issue date

01/10/2017

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