We introduce continuously additive models, which can be viewed as extensions of additive regression models with vector predictors to the case of infinite-dimensional predictors. This approach produces a class of flexible functional nonlinear regression models, where random predictor curves are...

We extend the common linear functional regression model to the case where the dependency of a scalar response on a functional predictor is of polynomial rather than linear nature. Focusing on the quadratic case, we demonstrate the usefulness of the polynomial functional regression model, which...

We consider the problem of estimating functional derivatives and gradients in the framework of a regression setting where one observes functional predictors and scalar responses. Derivatives are then defined as functional directional derivatives that indicate how changes in the predictor...