Optimal design of experiments for functional linear models with dynamic factors.

Caterina May, Theodoros Ladas, Davide Pigoli, Kalliopi Mylona

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Article in Test (Madrid, Spain), 2026. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.

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4 authors.

Caterina MayDepartment of Mathematics, King's College London, Strand Campus, London, WC2R 2LS UK.ORCID 0000-0002-0608-0238

Theodoros LadasDepartment of Mathematics, King's College London, Strand Campus, London, WC2R 2LS UK.ORCID 0009-0003-0583-889X

Davide PigoliDepartment of Mathematics, King's College London, Strand Campus, London, WC2R 2LS UK.ORCID 0000-0003-4591-4167

Kalliopi MylonaDepartment of Mathematics, King's College London, Strand Campus, London, WC2R 2LS UK.ORCID 0000-0002-1460-0715

Funding

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6 · The paper itself

Abstract

In this work, we build optimal experimental designs for precise estimation of the functional coefficient of linear regression model where both the response and the factors are continuous functions. After obtaining the variance-covariance matrix of the estimator of the functional coefficient which minimizes the integrated sum of square of errors, we extend the classical definition of optimal design to this estimator, and we provide the expression of the A-optimal and of the D-optimal designs. Examples of optimal designs for dynamic experimental factors are then computed through a suitable algorithm, and we discuss different scenarios in terms of the set of basis functions used for their representation. Finally, we present an illustrative example inspired by a real application in a pharmaceutical manufacturing process, to illustrate the feasibility and the advantages of our methodology.

Indexed as

Dynamic experimental conditionsEstimationFunctional data analysisFunction-on-function linear modelOptimal design of experiments

Identifiers

PMID42544130

DOI10.1007/s11749-026-01004-z

PMCPMC13427834

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LicenceCC BY

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