Kernel smoothing on manifolds
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866909999022735360 |
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| author | Bae, Eunseong Polonik, Wolfgang |
| author_facet | Bae, Eunseong Polonik, Wolfgang |
| contents | Under the assumption that data lie on a compact (unknown) manifold without boundary, we derive finite sample bounds for kernel smoothing and its (first and second) derivatives, and we establish asymptotic normality through Berry-Esseen type bounds. Special cases include kernel density estimation, kernel regression and the heat kernel signature. Connections to the graph Laplacian are also discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16777 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Kernel smoothing on manifolds Bae, Eunseong Polonik, Wolfgang Statistics Theory Machine Learning Differential Geometry Under the assumption that data lie on a compact (unknown) manifold without boundary, we derive finite sample bounds for kernel smoothing and its (first and second) derivatives, and we establish asymptotic normality through Berry-Esseen type bounds. Special cases include kernel density estimation, kernel regression and the heat kernel signature. Connections to the graph Laplacian are also discussed. |
| title | Kernel smoothing on manifolds |
| topic | Statistics Theory Machine Learning Differential Geometry |
| url | https://arxiv.org/abs/2601.16777 |