Spatial Principal Component Analysis and Moran Statistics for Multivariate Functional Areal Data
Abstract
This study presents the development of multivariate functional Moran's I, along with a novel approach termed multivariate functional areal spatial principal component analysis (mfasPCA), specifically designed for analyzing functional areal data. In addition, we propose a functional permutation-based testing framework that integrates (i) omnibus tests to detect spatial dependence within both positive and negative subspaces, (ii) component wise per-eigen tests that incorporate Holm's method to control the family-wise error rate, and (iii) a sequential rank-wise testing procedure. Through comprehensive simulation studies and an application to empirical data, we demonstrate the efficacy of multivariate functional Moran's I, mfasPCA, and the proposed testing framework in accurately assessing spatial autocorrelation and structural patterns in functional areal data.
Cite
@article{arxiv.2408.08630,
title = {Spatial Principal Component Analysis and Moran Statistics for Multivariate Functional Areal Data},
author = {Dharini Pathmanathan and Issa-Mbenard Dabo and Tzung Hsuen Khoo and Alaa Ali-Hassan and Sophie Dabo-Niang},
journal= {arXiv preprint arXiv:2408.08630},
year = {2026}
}