On boundary detection
Résumé
Given a sample of a random variable supported by a smooth compact manifold M ⊂ R d , 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 k n −nearest neighbors. We prove that the level of the test can be estimated, that, with probability one, the power is one for n large enough and that there exists consistent decision rule. A heuristic for choosing a convenient value for the k n parameter is also given. Finally we provide a simulation study of the test.
Domaines
Statistiques [math.ST]
Origine : Fichiers produits par l'(les) auteur(s)