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Modeling Repeated Functional Observations


  • Kehui Chen
  • Hans-Georg Müller


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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    References listed on IDEAS

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    2. Nikolay Nenovsky & S. Statev, 2006. "Introduction," Post-Print halshs-00260898, HAL.
    3. Jianqing Fan, 2000. "Simultaneous Confidence Bands and Hypothesis Testing in Varying-coefficient Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(4), pages 715-731.
    4. H rdle, Wolfgang & Huet, Sylvie & Mammen, Enno & Sperlich, Stefan, 2004. "Bootstrap Inference In Semiparametric Generalized Additive Models," Econometric Theory, Cambridge University Press, vol. 20(02), pages 265-300, April.
    5. Jing Wang & Lijian Yang, 2009. "Efficient and fast spline-backfitted kernel smoothing of additive models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(3), pages 663-690, September.
    6. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, March.
    7. Osmani, R.S., 1990. "Food Deprivation and Undernutrition in Rural Bangladesh," Research Paper 82, World Institute for Development Economics Research.
    8. Gerda Claeskens & Tatyana Krivobokova & Jean D. Opsomer, 2009. "Asymptotic properties of penalized spline estimators," Biometrika, Biometrika Trust, vol. 96(3), pages 529-544.
    9. Haerdle,Wolfgang & Bowman,Adrian, 1986. "Bootstrapping in nonparametric regression: Local adaptive smoothing and confidence bands," Discussion Paper Serie A 71, University of Bonn, Germany.
    10. M. Ruth & K. Donaghy & P. Kirshen, 2006. "Introduction," Chapters,in: Regional Climate Change and Variability, chapter 1 Edward Elgar Publishing.
    11. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, March.
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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:bla:jorssb:v:79:y:2017:i:1:p:177-196 is not listed on IDEAS
    3. 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.

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