Dimension reduction for functional regression with a binary response

• Published in: Statistical papers (Berlin, Germany) Vol. 62; no. 1; pp. 193 - 208
• Main Authors: Wang, Guochang, Liang, Beiting, Wang, Hansheng, Zhang, Baoxue, Xie, Baojian
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2021; Springer Nature B.V
• Subjects: Bayesian analysis; Computer simulation; Covariance; Economic Theory/Quantitative Economics/Mathematical Methods; Economics; Finance; Insurance; Management; Mathematics and Statistics; Operations Research/Decision Theory; Probability Theory and Stochastic Processes; Reduction; Regression; Regression analysis; Regular Article; Slicing; Statistics; Statistics for Business; Binary response; Dimension reduction; Functional data; Functional sufficient dimension reduction; Sliced inverse regression
• ISSN: 0932-5026; 1613-9798
• DOI: 10.1007/s00362-019-01083-1

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.