On boundary detection

Abstract : 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.
Type de document :
Pré-publication, Document de travail
2017
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https://hal.archives-ouvertes.fr/hal-01291996
Contributeur : Catherine Aaron <>
Soumis le : vendredi 7 juillet 2017 - 15:40:23
Dernière modification le : mardi 11 juillet 2017 - 01:11:48

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  • HAL Id : hal-01291996, version 2

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Catherine Aaron, Alejandro Cholaquidis. On boundary detection. 2017. <hal-01291996v2>

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