Kernel smoothing on manifolds
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.
Fields of Study & Subjects
Topological and Geometric Data Analysis
Geometric Analysis and Curvature Flows
Probability and Statistical Research
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 23 January 2026
- Document type
- Preprint