Statistical Consistency of Kernel Canonical Correlation Analysis
The Journal of Machine Learning Research
Functional-coefficient partially linear regression model
Journal of Multivariate Analysis
Successive direction extraction for estimating the central subspace in a multiple-index regression
Journal of Multivariate Analysis
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Functional data are infinite-dimensional statistical objects which pose significant challenges to both theorists and practitioners. Both parametric and nonparametric regressions have received attention in the functional data analysis literature. However, the former imposes stringent constraints while the latter suffers from logarithmic convergence rates. In this article, we consider two popular sufficient dimension reduction methods in the context of functional data analysis, which, if desired, can be combined with low-dimensional nonparametric regression in a later step. In computation, predictor processes and index vectors are approximated in finite dimensional spaces using the series expansion approach. In theory, the basis used can be either fixed or estimated, which include both functional principal components and B-spline basis. Thus our study is more general than previous ones. Numerical results from simulations and a real data analysis are presented to illustrate the methods.