Local convex hull support and boundary estimation

Baíllo, 2000, Set estimation and nonparametric detection, Canad. J. Statist., 28, 765, 10.2307/3315915 Bárány, 1992, Random polytopes in smooth convex bodies, Mathematika, 39, 81, 10.1112/S0025579300006872 Biau, 2009, Asymptotic normality in density support estimation, Electron. J. Probab., 14, 2617, 10.1214/EJP.v14-722 J.D. Boissonnat, A. Ghosh, Manifold reconstruction using tangential Delaunay complexes, in: Proceedings of the 26th Annual Symposium on Computational Geometry, 2010. Bubenik, 2010, Statistical topology via Morse theory, persistence, and nonparametric estimation, vol. 516 (91), 75 Carlsson, 2005, Persistent homology and the analysis of high dimensional data Carlsson, 2009, Topology and data, Bull. Amer. Math. Soc., 46, 255, 10.1090/S0273-0979-09-01249-X Carlsson, 2005, Persistence barcodes for shapes, Int. J. Shape Model., 11, 149, 10.1142/S0218654305000761 Chevalier, 1976, Estimation du support et du contour du support d’une loi de probabilité, Ann. Inst. H. Poincaré (B) Probab. Statist., 12, 339 Cholaquidis, 2014, On Poincaré cone property, Ann. Statist., 42, 255, 10.1214/13-AOS1188 Cuevas, 1990, On pattern analysis in the non-convex case, Kybernetes, 19, 26, 10.1108/eb005866 Cuevas, 2004, On boundary estimation, Adv. Appl. Probab., 36, 340, 10.1239/aap/1086957575 Devroye, 1980, Detection of abnormal behavior via nonparametric estimation of the support, SIAM J. Appl. Math., 38, 480, 10.1137/0138038 Dumbgen, 1996, Rates of convergence for random approximations of convex sets, Adv. Appl. Probab., 28, 384, 10.2307/1428063 Edelsbrunner, 1997, Triangulating topological spaces, Internat. J. Comput. Geom. Appl., 7, 365, 10.1142/S0218195997000223 Efron, 1965, The convex hull of a random set of points, Biometrika, 15, 331, 10.1093/biomet/52.3-4.331 Federer, 1959, Curvature measures, Trans. Amer. Math. Soc., 93, 418, 10.1090/S0002-9947-1959-0110078-1 Getz, 2004, A local nearest-neighbor convex-hull construction of home ranges and utilization distributions, Ecography, 27, 489, 10.1111/j.0906-7590.2004.03835.x Hardle, 1995, Estimation of non-sharp support boundaries, J. Multivariate Anal., 55, 205, 10.1006/jmva.1995.1075 Kesler, 2012, Foraging habitat distributions affect territory size and shape in the Tuamotu Kingfisher, Int. J. Zool., 2012, 10.1155/2012/632969 Khünel, 2005 Korte, 2008, Habitat selection at two spatial scales and diurnal activity patterns of adult female forest buffalo, J. Mammal., 89, 115, 10.1644/06-MAMM-A-423.1 Liu, 2010, Foraging habitats and utilization distributions of black-necked cranes wintering at the napahai wetland, China, J. Field Ornithol., 81, 21, 10.1111/j.1557-9263.2009.00257.x Penrose, 1999, A strong law for the largest nearest-neighbour link between random points, J. Lond. Math. Soc. (2), 60, 951, 10.1112/S0024610799008157 Reitzner, 2003, Random polytopes and the Efron–Stein Jackknife inequality, Ann. Probab., 31, 2136, 10.1214/aop/1068646381 Rodríguez-Casal, 2007, Set estimation under convexity type assumptions, Ann. Inst. H. Poincaré (B) Probab. Statist., 43, 763, 10.1016/j.anihpb.2006.11.001 Schneider, 1988, Random approximation of convex sets, J. Microsc., 151, 211, 10.1111/j.1365-2818.1988.tb04682.x Walther, 1999, On a generalization of Blaschke’s rolling theorem and the smoothing of surfaces, Math. Methods Appl. Sci., 22, 301, 10.1002/(SICI)1099-1476(19990310)22:4<301::AID-MMA42>3.0.CO;2-M Zomorodian, 2005, Computing persistent homology, Discrete Comput. Geom., 33, 247, 10.1007/s00454-004-1146-y