Issue |
ESAIM: PS
Volume 20, 2016
|
|
---|---|---|
Page(s) | 332 - 348 | |
DOI | https://doi.org/10.1051/ps/2016015 | |
Published online | 23 September 2016 |
A fully data-driven method for estimating the shape of a point cloud
Department of Statistics and Operations Research, University of Santiago de Compostela, Spain.
paula.saavedra@usc.es
Received: 11 August 2015
Revised: 11 April 2016
Accepted: 23 May 2016
Given a random sample of points from some unknown distribution, we propose a new data-driven method for estimating its probability support S. Under the mild assumption that S is r-convex, the smallest r-convex set which contains the sample points is the natural estimator. The main problem for using this estimator in practice is that r is an unknown geometric characteristic of the set S. A stochastic algorithm is proposed for selecting its optimal value from the data under the hypothesis that the sample is uniformly generated. The new data-driven reconstruction of S is able to achieve the same convergence rates as the convex hull for estimating convex sets, but under a much more flexible smoothness shape condition.
Mathematics Subject Classification: 62G05 / 62G20
Key words: Support estimation / r-convexity / uniformity / maximal spacing
© EDP Sciences, SMAI, 2016
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.