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Modeling Repeated Functional Observations

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  • Kehui Chen
  • Hans-Georg Müller

Abstract

We introduce a new methodological framework for repeatedly observed and thus dependent functional data, aiming at situations where curves are recorded repeatedly for each subject in a sample. Our methodology covers the case where the recordings of the curves are scheduled on a regular and dense grid and also situations more typical for longitudinal studies, where the timing of recordings is often sparse and random. The proposed models lead to an interpretable and straightforward decomposition of the inherent variation in repeatedly observed functional data and are implemented through a straightforward two-step functional principal component analysis. We provide consistency results and asymptotic convergence rates for the estimated model components. We compare the proposed model with an alternative approach via a two-dimensional Karhunen-Loève expansion and illustrate it through the analysis of longitudinal mortality data from period lifetables that are repeatedly observed for a sample of countries over many years, and also through simulation studies. This article has online supplementary materials.

Suggested Citation

  • Kehui Chen & Hans-Georg Müller, 2012. "Modeling Repeated Functional Observations," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1599-1609, December.
  • Handle: RePEc:taf:jnlasa:v:107:y:2012:i:500:p:1599-1609
    DOI: 10.1080/01621459.2012.734196
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    File URL: http://hdl.handle.net/10.1080/01621459.2012.734196
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    1. repec:spr:stabio:v:9:y:2017:i:2:d:10.1007_s12561-015-9137-5 is not listed on IDEAS
    2. repec:eee:jmvana:v:165:y:2018:i:c:p:279-295 is not listed on IDEAS
    3. repec:bla:jorssb:v:79:y:2017:i:1:p:177-196 is not listed on IDEAS
    4. Kehui Chen & Xiaoke Zhang & Alexander Petersen & Hans-Georg Müller, 0. "Quantifying Infinite-Dimensional Data: Functional Data Analysis in Action," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 0, pages 1-23.
    5. Mark J. Meyer & Brent A. Coull & Francesco Versace & Paul Cinciripini & Jeffrey S. Morris, 2015. "Bayesian function-on-function regression for multilevel functional data," Biometrics, The International Biometric Society, vol. 71(3), pages 563-574, September.

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