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

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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.

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Authors and Affiliations

  1. The Center for Applied Statistics, Institute of Statistics and Big Data, Renmin University of China, Beijing, 100872, China

    Shirun Shen, Huiya Zhou & Kejun He

  2. Department of Statistics, Texas A &M University, College Station, TX, 77843-3143, USA

    Lan Zhou

Authors
  1. Shirun Shen
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  2. Huiya Zhou
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  3. Kejun He
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  4. Lan Zhou
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Correspondence to Kejun He.

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This article was majorly completed while Shirun Shen was a Ph.D. candidate in Department of Statistics, Texas A &M University. This research was supported by Public Computing Cloud, Renmin University of China.

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Supplementary file 1 (pdf 267 KB)

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Shen, S., Zhou, H., He, K. et al. Principal Component Analysis of Two-dimensional Functional Data with Serial Correlation. JABES (2023). https://doi.org/10.1007/s13253-023-00585-8

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  • DOI: https://doi.org/10.1007/s13253-023-00585-8

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