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Local and global temporal correlations for longitudinal data

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  • Zhou, Yang
  • Lin, Shu-Chin
  • Wang, Jane-Ling

Abstract

Quantifying the association between a pair of random functions recorded over a time period is of general interest. Several methods have been proposed in the literature but they either suffer from an ill-posed problem intrinsic to functional data or are suitable only for intensely recorded longitudinal data. In this paper we provide new methods that overcome these challenges by investigating the temporal Pearson correlation between paired random functions. We investigate both a local temporal correlation measure and a global summary measure of the dynamic temporal correlations and propose a nonparametric estimation method that covers both intensely observed and sparsely observed longitudinal data. Asymptotic results of the estimators are derived under mild conditions and the method is illustrated via simulations and a benchmark data set.

Suggested Citation

  • Zhou, Yang & Lin, Shu-Chin & Wang, Jane-Ling, 2018. "Local and global temporal correlations for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 1-14.
    • Handle: RePEc:eee:jmvana:v:167:y:2018:i:c:p:1-14
    DOI: 10.1016/j.jmva.2018.03.015
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    References listed on IDEAS

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    1. He, Guozhong & Müller, Hans-Georg & Wang, Jane-Ling, 2003. "Functional canonical analysis for square integrable stochastic processes," Journal of Multivariate Analysis, Elsevier, vol. 85(1), pages 54-77, April.
    2. Cupidon, J. & Eubank, R. & Gilliam, D. & Ruymgaart, F., 2008. "Some properties of canonical correlations and variates in infinite dimensions," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1083-1104, July.
    3. Wenjing Yang & Hans‐Georg Müller & Ulrich Stadtmüller, 2011. "Functional singular component analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(3), pages 303-324, June.
    4. Shin, Hyejin & Lee, Seokho, 2015. "Canonical correlation analysis for irregularly and sparsely observed functional data," Journal of Multivariate Analysis, Elsevier, vol. 134(C), pages 1-18.
    5. Yao, Fang & Muller, Hans-Georg & Wang, Jane-Ling, 2005. "Functional Data Analysis for Sparse Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 577-590, June.
    6. Eubank, R.L. & Hsing, Tailen, 2008. "Canonical correlation for stochastic processes," Stochastic Processes and their Applications, Elsevier, vol. 118(9), pages 1634-1661, September.
    7. Dubin, Joel A. & Muller, Hans-Georg, 2005. "Dynamical Correlation for Multivariate Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 872-881, September.
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    Cited by:

    1. Zhang, Jin-Ting & Zhu, Tianming, 2024. "A fast and accurate kernel-based independence test with applications to high-dimensional and functional data," Journal of Multivariate Analysis, Elsevier, vol. 202(C).

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