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.
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https://hal.archives-ouvertes.fr/hal-01291996
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Submitted on : Thursday, July 4, 2019 - 1:45:19 PM
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Catherine Aaron, Alejandro Cholaquidis. On boundary detection. 2019. ⟨hal-01291996v3⟩

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