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 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...