  Predicting scalar outcomes using functional predictors is a classic problem
in functional data analysis. In many applications, however, only specific
locations or time-points of the functional predictors have an impact on the
outcome. Such ``points of impact'' are typically unknown and have to be
estimated in addition to estimating the usual model components. We show that
our points of impact estimator enjoys a super-consistent convergence rate and
does not require knowledge or pre-estimates of the unknown model components.
This remarkable result facilitates the subsequent estimation of the remaining
model components as shown in the theoretical part, where we consider the case
of nonparametric models and the practically relevant case of generalized linear
models. The finite sample properties of our estimators are assessed by means of
a simulation study. Our methodology is motivated by data from a psychological
experiment in which the participants were asked to continuously rate their
emotional state while watching an affective video eliciting a varying intensity
of emotional reactions.
