A-optimal Designs of Experiments in Linear Models with Dynamic Factors and Functional Responses

Optimal design of experiments with functional data is a novel and highly relevant research topic. We illustrate here a recent work which considers linear models where both the response and one or more factors are continuous functions, for example, of the time. The goal is to find the optimal dynamic experimental conditions to estimate precisely the functional coefficients of the model. After establishing a suitable estimator and obtaining its variance-covariance matrix, the definition of optimal design criteria is extended to the functional data context. In this short paper, some additional examples and numerical results on A-optimal dynamic designs are provided, with the choice of suitable bases of functions to represent the data. The efficiency of estimators is compared under various choices of bases.