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arXiv · 2408.08630

Spatial Principal Component Analysis and Moran Statistics for Multivariate Functional Areal Data

Dharini Pathmanathan·Issa-Mbenard Dabo·Tzung Hsuen Khoo·Alaa Ali-Hassan·Sophie Dabo-Niang
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Abstract

The paper introduces a multivariate functional areal spatial principal component analysis (mfasPCA) framework, together with multivariate functional Moran's I statistics, to enable the assessment of spatial autocorrelation and dimension reduction for multivariate functional data observed over areal units. The proposed framework is spatial-functional in scope: the functional argument may represent time, age, wavelength, or another ordered continuum, while spatial dependence is introduced across areal units through a spatial weight matrix. The principal component method is defined through a Moran-type spatially weighted criterion. We propose eigenvalue-based permutation tests to assess the significance of spatially structured components. The testing framework includes omnibus tests, componentwise tests with Holm adjustment, and sequential rank-wise tests based on tail sums of eigenvalues. Simulation studies show that mfasPCA captures positive and negative spatial-functional structures and concentrates them in the leading components under the respective autocorrelation regimes. A real-data application illustrates how mfasPCA identifies spatially structured modes of multivariate functional variation.

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Dharini Pathmanathan, Issa-Mbenard Dabo, Tzung Hsuen Khoo, Alaa Ali-Hassan, Sophie Dabo-Niang. 2024-08-16. Spatial Principal Component Analysis and Moran Statistics for Multivariate Functional Areal Data. https://arxiv.org/abs/2408.08630

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