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

Shirun Shen, Huiya Zhou, Kejun He () and Lan Zhou
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Shirun Shen: Renmin University of China
Huiya Zhou: Renmin University of China
Kejun He: Renmin University of China
Lan Zhou: Texas A &M University

Journal of Agricultural, Biological and Environmental Statistics, 2024, vol. 29, issue 3, No 10, 620 pages

Abstract: 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.

Keywords: Bivariate splines; EM algorithm; Functional principal component analysis; Kalman filter and smoother; Triangulation (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13253-023-00585-8

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