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Abstract:
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Regression models to relate a scalar, Y, to a functional predictor, X(t), are becoming increasingly common. Work in this area has concentrated on estimating a coefficient function, beta(t), with Y related to X through the integral of beta(t) multiplied by X(t). A significant issue in the functional domain is that of producing an interpretable beta curve and several papers have recently been written on methods to generate curves with simple structure. In this talk we propose an approach for extending one of these procedures to the functional generalized linear models paradigm. This allows one to produce interpretable beta curves for a much wider class of situations, including classification problems such as logistic regression. We demonstrate our method on different data sets. In addition, interesting nonasymptotic theoretical bounds on the estimation error are presented.
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