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Title: Estimation of points of impact in nonparametric regression with functional predictors Authors:  Dominik Poss - University of Bonn (Germany)
Dominik Liebl - University Bonn (Germany) [presenting]
Alois Kneip - University of Bonn (Germany)
Abstract: In many applications only specific locations or time-points of functional predictors have an impact on the outcome. The selection of such points of impact constitutes a particular variable selection problem, since the high correlation in the functional predictors violates the basic assumptions of existing high-dimensional variable selection procedures. We introduce a method to estimate points of impact in nonparametric regression models. We propose a threshold-based and a fully data-driven estimator and show that the point of impact estimators can be estimated with a super-consistent convergence rate for a large class of functional data processes. The finite sample properties of our estimators are assessed by means of a simulation study. Our methodology is motivated by a psychological case study in which the participants were asked to continuously rate their emotional state while watching an affective online video on the persecution of African albinos.