Level set and density estimation on manifolds
Resumen:
We tackle the problem of the estimation of the level sets Lf (λ) of the density f of a random vector X supported on a smooth manifold M ⊂ Rd, from an iid sample of X. To do that we introduce a kernel-based estimator ˆfn,h, which is a slightly modified version of the one proposed in [45], and proves its a.s. uniform convergence to f . Then, we propose two estimators of Lf (λ), the first one is a plug-in: L ˆfn,h (λ), which is proven to be a.s. consistent in Hausdorff distance and distance in measure, if Lf (λ) does not meet the boundary of M . While the second one assumes that Lf (λ) is r-convex, and is estimated by means of the r-convex hull of L ˆfn,h (λ). The performance of our proposal is illustrated through some simulated examples. In a real data example we analyze the intensity and direction of strong and moderate winds.
| 2021 | |
| ANII: FCE_1_2019_1_156054 | |
| Mathematics - Statistics theory | |
| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/37378 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| Sumario: | Publicado también en: Journal of Multivariate Analysis, 2022, 189: 104925. DOI: 10.1016/j.jmva.2021.104925 |
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