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Principal Component Analysis of Two-dimensional Functional Data with Serial Correlation

Author

Listed:
  • Shirun Shen

    (Renmin University of China)

  • Huiya Zhou

    (Renmin University of China)

  • Kejun He

    (Renmin University of China)

  • Lan Zhou

    (Texas A &M University)

Abstract

In this paper, we propose a novel model to analyze serially correlated two-dimensional functional data observed sparsely and irregularly on a domain which may not be a rectangle. Our approach employs a mixed effects model that specifies the principal component functions as bivariate splines on triangles and the principal component scores as random effects which follow an auto-regressive model. We apply the thin-plate penalty for regularizing the bivariate function estimation and develop an effective EM algorithm along with Kalman filter and smoother for calculating the penalized likelihood estimates of the parameters. Our approach was applied on simulated datasets and on Texas monthly average temperature data from January year 1915 to December year 2014. Supplementary materials accompanying this paper appear online.

Suggested Citation

  • Shirun Shen & Huiya Zhou & Kejun He & Lan Zhou, 2024. "Principal Component Analysis of Two-dimensional Functional Data with Serial Correlation," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 29(3), pages 601-620, September.
    • Handle: RePEc:spr:jagbes:v:29:y:2024:i:3:d:10.1007_s13253-023-00585-8
    DOI: 10.1007/s13253-023-00585-8
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    References listed on IDEAS

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