In this work we study the theory of optimal design of experiments when functional observations occur. We provide the best estimate for the functional coefficient in a linear model with functional response and multivariate predictor, exploiting fully the information provided by both functions and derivatives. We define different optimality criteria for the estimate of a functional coefficient. Then, we provide a strong theoretical foundation to prove that the computation of these optimal designs, in the case of linear models, is the same as in the classical theory, but a different interpretation needs to be given.
On Applying Optimal Design of Experiments when Functional Observations Occur / G. Aletti, C. May, C. Tommasi (CONTRIBUTIONS TO STATISTICS). - In: mODa 11 : Advances in Model-Oriented Design and Analysis / [a cura di] J. Kunert, C.H. MRuller, A.C. Atkinson. - Prima edizione. - [s.l] : Springer, 2016. - ISBN 9783319312644. - pp. 1-9 (( Intervento presentato al 11. convegno International Workshop in Model-Oriented Design and Analysis tenutosi a Hamminkeln nel 2016 [10.1007/978-3-319-31266-8_1].
On Applying Optimal Design of Experiments when Functional Observations Occur
G. AlettiPrimo
;C. TommasiUltimo
2016
Abstract
In this work we study the theory of optimal design of experiments when functional observations occur. We provide the best estimate for the functional coefficient in a linear model with functional response and multivariate predictor, exploiting fully the information provided by both functions and derivatives. We define different optimality criteria for the estimate of a functional coefficient. Then, we provide a strong theoretical foundation to prove that the computation of these optimal designs, in the case of linear models, is the same as in the classical theory, but a different interpretation needs to be given.File | Dimensione | Formato | |
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