Choosing the Right Norm for Change Point Detection in Functional Data
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909453508411392 |
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| author | Bastian, Patrick |
| author_facet | Bastian, Patrick |
| contents | We consider the problem of detecting a change point in a sequence of mean functions from a functional time series. We propose an $L^1$ norm based methodology and establish its theoretical validity both for classical and for relevant hypotheses. We compare the proposed method with currently available methodology that is based on the $L^2$ and supremum norms. Additionally we investigate the asymptotic behaviour under the alternative for all three methods and showcase both theoretically and empirically that the $L^1$ norm achieves the best performance in a broad range of scenarios. We also propose a power enhancement component that improves the performance of the $L^1$ test against sparse alternatives. Finally we apply the proposed methodology to both synthetic and real data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_04476 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Choosing the Right Norm for Change Point Detection in Functional Data Bastian, Patrick Statistics Theory Methodology 60F17, 62R10, 62M10 We consider the problem of detecting a change point in a sequence of mean functions from a functional time series. We propose an $L^1$ norm based methodology and establish its theoretical validity both for classical and for relevant hypotheses. We compare the proposed method with currently available methodology that is based on the $L^2$ and supremum norms. Additionally we investigate the asymptotic behaviour under the alternative for all three methods and showcase both theoretically and empirically that the $L^1$ norm achieves the best performance in a broad range of scenarios. We also propose a power enhancement component that improves the performance of the $L^1$ test against sparse alternatives. Finally we apply the proposed methodology to both synthetic and real data. |
| title | Choosing the Right Norm for Change Point Detection in Functional Data |
| topic | Statistics Theory Methodology 60F17, 62R10, 62M10 |
| url | https://arxiv.org/abs/2501.04476 |