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Combining Concurrent and Historical Functional Linear Regression

joint work with Alois Kneip and Dominik Liebl

Abstract: A new function-on-function linear regression model that incorporates common and point effects of a regressor function on a response function is introduced. The model comprises two components: a Hilbert-Schmidt integral operator for the common component and a concurrent component that captures the regressor’s impact on the response at each domain point. The identification of the model is discussed, proposing a smoothing spline estimator, providing asymptotic theory, and demonstrating its practicality using sports data.

Working paper coming soon.