Dimension reduction for functional regression with a binary response

  • Guochang Wang
  • Beiting Liang
  • Hansheng Wang
  • Baoxue ZhangEmail author
  • Baojian Xie
Regular Article


We propose here a novel functional inverse regression method (i.e., functional surrogate assisted slicing) for functional data with binary responses. Previously developed method (e.g., functional sliced inverse regression) can detect no more than one direction in the functional sufficient dimension reduction subspace. In contrast, the proposed new method can detect multiple directions. The population properties of the proposed method is established. Furthermore, we propose a new method to estimate the functional central space which do not need the inverse of the covariance operator. To practically determine the structure dimension of the functional sufficient dimension reduction subspace, a modified Bayesian information criterion method is proposed. Numerical studies based on both simulated and real data sets are presented.


Binary response Dimension reduction Functional sufficient dimension reduction Functional data Sliced inverse regression 



The authors are very thankful to the Editor, Associate Editor, and a reviewer for their constructive comments and suggestions, which have helped significantly in improving the paper. Guochang Wang’s research was supported by NSFC 11501248 from the National Science Foundation of China and from the Fundamental Research Funds for the Central Universities, Baoxue Zhang’s research was supported by NSFC 11671268 from the National Science Foundation of China.

Supplementary material

362_2019_1083_MOESM1_ESM.txt (239 kb)
Supplementary material 1 (txt 239 KB)


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Guochang Wang
    • 1
  • Beiting Liang
    • 1
  • Hansheng Wang
    • 2
  • Baoxue Zhang
    • 3
    Email author
  • Baojian Xie
    • 1
  1. 1.College of EconomicsJinan UniversityGuangzhouPeople’s Republic of China
  2. 2.Guanghua School of ManagementPeking UniversityBeijingPeople’s Republic of China
  3. 3.School of StatisticsUniversity of Economics and BusinessBeijingPeople’s Republic of China

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