Optimal designs for experiments for scalar-on-function linear models
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The aim of this work is to extend the usual optimal experimental design paradigm to experiments where the settings of one or more factors are functions. For these new experiments, a design consists of combinations of functions for each run of the experiment along with settings for non-functional variables. After briefly introducing the class of functional variables, basis function systems are described. Basis function expansion is applied to a functional linear model consisting of both functional and scalar factors, reducing the problem to an optimisation problem of a single design matrix.
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