Given a random sample of points from some unknown distribution, we propose a new data-driven method for estimating its probability support . Under the mild assumption that is -convex, the smallest -convex set which contains the sample points is the natural estimator. The main problem for using this estimator in practice is that is an unknown geometric characteristic of the set . 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 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.
Accepté le :
DOI : 10.1051/ps/2016015
Mots clés : Support estimation, r-convexity, uniformity, maximal spacing
@article{PS_2016__20__332_0,
author = {Rodr{\'\i}guez-Casal, A. and Saavedra-Nieves, P.},
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},
volume = {20},
year = {2016},
doi = {10.1051/ps/2016015},
zbl = {1357.62228},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ps/2016015/}
}
TY - JOUR AU - Rodríguez-Casal, A. AU - Saavedra-Nieves, P. TI - A fully data-driven method for estimating the shape of a point cloud JO - ESAIM: Probability and Statistics PY - 2016 SP - 332 EP - 348 VL - 20 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps/2016015/ DO - 10.1051/ps/2016015 LA - en ID - PS_2016__20__332_0 ER -
%0 Journal Article %A Rodríguez-Casal, A. %A Saavedra-Nieves, P. %T A fully data-driven method for estimating the shape of a point cloud %J ESAIM: Probability and Statistics %D 2016 %P 332-348 %V 20 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ps/2016015/ %R 10.1051/ps/2016015 %G en %F PS_2016__20__332_0
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. http://www.numdam.org/articles/10.1051/ps/2016015/
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