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Principal Component Analysis of Spatially Indexed Functions

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  • Thomas Kuenzer
  • Siegfried Hörmann
  • Piotr Kokoszka

Abstract

We develop an expansion, similar in some respects to the Karhunen–Loève expansion, but which is more suitable for functional data indexed by spatial locations on a grid. Unlike the traditional Karhunen–Loève expansion, it takes into account the spatial dependence between the functions. By doing so, it provides a more efficient dimension reduction tool, both theoretically and in finite samples, for functional data with moderate spatial dependence. For such data, it also possesses other theoretical and practical advantages over the currently used approach. The article develops complete asymptotic theory and estimation methodology. The performance of the method is examined by a simulation study and data analysis. The new tools are implemented in an R package. Supplementary materials for this article are available online.

Suggested Citation

  • Thomas Kuenzer & Siegfried Hörmann & Piotr Kokoszka, 2021. "Principal Component Analysis of Spatially Indexed Functions," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(535), pages 1444-1456, July.
    • Handle: RePEc:taf:jnlasa:v:116:y:2021:i:535:p:1444-1456
    DOI: 10.1080/01621459.2020.1732395
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    Cited by:

    1. Alexander Gleim & Nazarii Salish, 2022. "Forecasting Environmental Data: An example to ground-level ozone concentration surfaces," Papers 2202.03332, arXiv.org.
    2. Tzung Hsuen Khoo & Dharini Pathmanathan & Sophie Dabo-Niang, 2023. "Spatial Autocorrelation of Global Stock Exchanges Using Functional Areal Spatial Principal Component Analysis," Mathematics, MDPI, vol. 11(3), pages 1-24, January.
    3. Dennis Schroers, 2024. "Robust Functional Data Analysis for Stochastic Evolution Equations in Infinite Dimensions," Papers 2401.16286, arXiv.org, revised Jun 2024.
    4. Cai, Leheng & Hu, Qirui, 2024. "Simultaneous inference and uniform test for eigensystems of functional data," Computational Statistics & Data Analysis, Elsevier, vol. 192(C).

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