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- Title
A FUNCTIONAL SINGLE-INDEX MODEL.
- Authors
Fei Jiang; Seungchul Baek; Jiguo Cao; Yanyuan Ma
- Abstract
We propose a semiparametric functional single-index model for studying the relationship between a univariate response and multiple functional covariates. The parametric part of the model integrates a functional linear regression model and a sufficient dimension-reduction structure. The nonparametric part of the model allows the response-index dependence or the link function to be unspecified. The B-spline method is used to approximate the coefficient function, which leads to a dimension-folding-type model. A new kernel regression method is developed to handle the dimension-folding model, allowing us to estimate the index vector and the B-spline coefficients efficiently. We also establish the asymptotic properties and semiparametric optimality for the estimators.
- Subjects
REGRESSION analysis; PARAMETRIC modeling; FUNCTIONAL analysis; DATA analysis; DEPENDENCE (Statistics)
- Publication
Statistica Sinica, 2020, Vol 30, Issue 1, p303
- ISSN
1017-0405
- Publication type
Article
- DOI
10.5705/ss.202018.0013