On Estimating the Perimeter Using the Alpha-Shape

Published 30 Jun 2015 in math.ST and stat.TH | (1507.00065v1)

Abstract: We consider the problem of estimating the perimeter of a smooth domain in the plane based on a sample from the uniform distribution over the domain. We study the performance of the estimator defined as the perimeter of the alpha-shape of the sample. Some numerical experiments corroborate our theoretical findings.

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