On boundary detection
Resumen:
Given a sample of a random variable supported by a smooth compact manifold M⊂Rd, we propose a test to decide whether the boundary of M is empty or not with no preliminary support estimation. The test statistic is based on the maximal distance between a sample point and the average of its kn-nearest neighbors. We prove that the level of the test can be estimated, that, with probability one, its power is one for n large enough, and that there exists a consistent decision rule. Heuristics for choosing a convenient value for the kn parameter and identifying observations close to the boundary are also given. We provide a simulation study of the test.
| 2019 | |
| ANII: FCE_1_2019_1_156054 | |
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Boundary Geometric inference Nearest-neighbors Test |
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| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/37391 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| Sumario: | Publicado también en: Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 2020, 56(3): 2028-2050. DOI: 10.1214/19-AIHP1027 |
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