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

2013/01/18 by Bo Markussen · 2 citations
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Acoustic Wave Phenomena Research #Matrix Theory and Algorithms #Model Reduction and Neural Networks #math.ST #stat.TH

paper · pdf · doi:10.3150/11-bej389

published as Bernoulli 2013, Vol. 19, No. 1, 1-17 · Published in at http://dx.doi.org/10.3150/11-BEJ389 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

openalex publication_date 2013/01/18 · arxiv created 2013/01/21 · arxiv updated 2013/01/22 · openalex created_date 2020/11/23 · openalex updated_date 2026/07/28

Abstract

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

Cited by

• A nonlinear mixed-effects model for simultaneous smoothing and registration of functional data
• Differential equations, splines and Gaussian processes

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• Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators
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