Geodesic
A fully data-driven method for estimating the shape of a point cloud
Rodríguez-Casal, A.1 ; Saavedra-Nieves, P.1
1 Department of Statistics and Operations Research, University of Santiago de Compostela, Spain.
ESAIM: Probability and Statistics, Tome 20 (2016), pp. 332-348

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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.

Reçu le :
Accepté le :
DOI : 10.1051/ps/2016015
Classification : 62G05, 62G20
Keywords: Support estimation, r-convexity, uniformity, maximal spacing

Rodríguez-Casal, A. 1 ; Saavedra-Nieves, P. 1

1 Department of Statistics and Operations Research, University of Santiago de Compostela, Spain. 
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     title = {A fully data-driven method for estimating the shape of a point cloud},
     journal = {ESAIM: Probability and Statistics},
     pages = {332--348},
     publisher = {EDP-Sciences},
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     year = {2016},
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     zbl = {1357.62228},
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Rodríguez-Casal, A.; Saavedra-Nieves, P. A fully data-driven method for estimating the shape of a point cloud. ESAIM: Probability and Statistics, Tome 20 (2016), pp. 332-348. doi: 10.1051/ps/2016015

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