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Functional data analysis in a mixed-effects model framework is done usingoperator calculus. In this approach the functional parameters are treated asserially correlated effects giving an alternative to the penalized likelihoodapproach, where the functional parameters are treated as fixed effects.Operator approximations for the necessary matrix computations are proposed, andsemi-explicit and numerically stable formulae of linear computationalcomplexity are derived for likelihood analysis. The operator approach rendersthe usage of a functional basis unnecessary and clarifies the role of theboundary conditions.

Functional data analysis in an operator-based mixed-model framework