Kernel smoothing on manifolds

Eunseong Bae; Wolfgang Polonik

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arXiv · 2601.16777

Kernel smoothing on manifolds

Eunseong Bae·Wolfgang Polonik

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Abstract

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.

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Eunseong Bae, Wolfgang Polonik. 2026-01-23. Kernel smoothing on manifolds. https://arxiv.org/abs/2601.16777

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