Estimation and inference in functional mixed-effects models

  • Authors:

  • Anestis Antoniadis;Theofanis Sapatinas

  • Affiliations:

  • Laboratoire IMAG-LMC, University Joseph Fourier, BP 53, 38041 Grenoble Cedex 9, France;Department of Mathematics and Statistics, University of Cyprus, P.O. Box 20537, CY 1678 Nicosia, Cyprus

  • Venue:
  • Computational Statistics & Data Analysis
  • Year:
  • 2007

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Abstract

Functional mixed-effects models are very useful in analyzing functional data. A general functional mixed-effects model that inherits the flexibility of linear mixed-effects models in handling complex designs and correlation structures is considered. A wavelet decomposition approach is used to model both fixed-effects and random-effects in the same functional space, meaning that the population-average curve and the subject-specific curves have the same smoothness property. A linear mixed-effects representation is then obtained that is used for estimation and inference in the general functional mixed-effects model. Adapting recent methodologies in linear mixed-effects and nonparametric regression models, hypothesis testing procedures for both fixed-effects and random-effects are provided. Using classical linear mixed-effects estimation techniques, the linear mixed-effects representation is also used to obtain wavelet-based estimates for both fixed-effects and random-effects in the general functional mixed-effects model. The usefulness of the proposed estimation and hypothesis testing procedures is illustrated by means of a small simulation study and a real-life dataset arising from physiology.