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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 B(t) with Y related to X(t) through the integral of B(t) multiplied by X(t). Points where B(t)< >0 correspond to points where there is a positive/negative relationship between X(t) and Y. Alternatively, points where B(t)=0 indicate no relationship. Hence, identification of these regions has important implications. Unfortunately, most fitting procedures result in a B(t) with unnatural wiggles, making the curve hard to interpret. In this talk, we introduce a new approach that borrows ideas from a new class of variable selection procedures to produce coefficient curves that have simple shapes. This approach greatly simplifies the interpretation of the relationship between X(t) and Y over different regions of t
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