Physical or biological processes can have input factors (such as temperature, pressure, etc.) that vary over time, i.e. they have a functional nature. If the output is also functional (such as activity or growth curves in biology or shape profiles in manufacturing), the relationship between the functional output and the dynamic factors can be modelled using function-on-function linear models.

In experimental settings, the functional form of the dynamic factors can be chosen by the experimenter, albeit with some constraints in terms of the complexity. In this talk, we will discuss how dynamic factors can be set in an optimal way to improve the accuracy of the estimators in function-on-function linear models. We will see how A-optimality and D-optimality (and their Bayesian versions) can be extended to this setting and what kinds of designs are optimal depending on the modelling choices on the functional objects.

This is joint work with Caterina May and Theodoros Ladas