Spatial Principal Component Analysis and Moran Statistics for Multivariate Functional Areal Data
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915952386375680 |
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| author | Pathmanathan, Dharini Dabo, Issa-Mbenard Khoo, Tzung Hsuen Ali-Hassan, Alaa Dabo-Niang, Sophie |
| author_facet | Pathmanathan, Dharini Dabo, Issa-Mbenard Khoo, Tzung Hsuen Ali-Hassan, Alaa Dabo-Niang, Sophie |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_08630 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spatial Principal Component Analysis and Moran Statistics for Multivariate Functional Areal Data Pathmanathan, Dharini Dabo, Issa-Mbenard Khoo, Tzung Hsuen Ali-Hassan, Alaa Dabo-Niang, Sophie Methodology 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. |
| title | Spatial Principal Component Analysis and Moran Statistics for Multivariate Functional Areal Data |
| topic | Methodology |
| url | https://arxiv.org/abs/2408.08630 |