2014/04/29 by Alberto Rodríguez-Casal, Rodríguez-Casal, Alberto, Paula Saavedra-Nieves +1
Mathematics · #Applications (stat.AP) #Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistics Theory (math.ST) #math.ST #stat.AP #stat.CO #stat.ME #stat.TH
paper · pdf · doi:10.48550/arxiv.1404.7397
29 pages
arxiv created 2014/11/27 · arxiv updated 2014/12/01
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 it 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. The practical performance of the estimator is illustrated through a real data example and a simulation study.