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A Confidence Corridor for Sparse Longitudinal Data Curves

Author

Listed:
  • Shuzhuan Zheng
  • Lijian Yang
  • Wolfgang Karl Härdle

Abstract

Longitudinal data analysis is a central piece of statistics. The data are curves and they are observed at random locations. This makes the construction of a simultaneous confidence corridor (SCC) (confidence band) for the mean function a challenging task on both the theoretical and the practical side. Here we propose a method based on local linear smoothing that is implemented in the sparse (i.e., low number of nonzero coefficients) modelling situation. An SCC is constructed based on recent results obtained in applied probability theory. The precision and performance is demonstrated in a spectrum of simulations and applied to growth curve data. Technically speaking, our paper intensively uses recent insights into extreme value theory that are also employed to construct a shoal of confidence intervals (SCI).

Suggested Citation

  • Shuzhuan Zheng & Lijian Yang & Wolfgang Karl Härdle, 2011. "A Confidence Corridor for Sparse Longitudinal Data Curves," SFB 649 Discussion Papers SFB649DP2011-002, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    • Handle: RePEc:hum:wpaper:sfb649dp2011-002
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    File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2011-002.pdf
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    References listed on IDEAS

    as
    1. Christine Cierco-Ayrolles & Alain Croquette & Céline Delmas, 2003. "Computing the Distribution of the Maximum of Gaussian Random Processes," Methodology and Computing in Applied Probability, Springer, vol. 5(4), pages 427-438, December.
    2. Yao, Fang, 2007. "Asymptotic distributions of nonparametric regression estimators for longitudinal or functional data," Journal of Multivariate Analysis, Elsevier, vol. 98(1), pages 40-56, January.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Longitudinal data; confidence band; Karhunen-Loève L² representation; local linear estimator; extreme value; double sum; strong approximation;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models

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