Dimension reduction for functional regression with a binary response

Guochang Wang, Beiting Liang, Hansheng Wang, Baoxue Zhang () and Baojian Xie
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Guochang Wang: Jinan University
Beiting Liang: Jinan University
Hansheng Wang: Peking University
Baoxue Zhang: University of Economics and Business
Baojian Xie: Jinan University

Statistical Papers, 2021, vol. 62, issue 1, No 10, 193-208

Abstract: Abstract 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.

Keywords: Binary response; Dimension reduction; Functional sufficient dimension reduction; Functional data; Sliced inverse regression (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00362-019-01083-1

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