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Abstract:
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This talk discusses a new type of functional regression model involving trajectories as predictors of univariate responses. The basic idea is to include time points among the parameters of interest, and to fit a (possibly mis-specified) model using just the values of the trajectories at those times. This provides greater interpretability than the functional linear regression approach that has become popular in recent years. The new methodology involves nonstandard asymptotic theory; specifically, non-Gaussian limit distributions and rates of convergence that are determined in some sense by the smoothness of the trajectories. In the case of trajectories that are single-jump counting processes, it specializes to an existing type of change-point analysis. Trajectories of diffusion-type are also studied in detail.
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