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Abstract:
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We develop a functional single-index model for functional data analysis, where both the response and multiple predictors are functions, and we assume the response is related to a linear combination of the predictors via an unknown link function. The proposed method greatly enhances the flexibility of functional linear models and provides a useful tool for dimension reduction in regression with multiple functional predictors. Assuming that the functional predictors are observed at discrete points, we use B-spline basis functions to estimate the index functions and the link function, and propose an iterative estimating procedure. Several numerical examples illustrate that the proposed model and estimation methodology are flexible and effective in practice.
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