Set estimation under convexity type assumptions
Rodríguez Casal, Alberto
Annales de l'I.H.P. Probabilités et statistiques, Tome 43 (2007), p. 763-774 / Harvested from Numdam
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Publié le : 2007-01-01
DOI : https://doi.org/10.1016/j.anihpb.2006.11.001 
@article{AIHPB_2007__43_6_763_0,
     author = {Rodr\'\i guez Casal, Alberto},
     title = {Set estimation under convexity type assumptions},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {43},
     year = {2007},
     pages = {763-774},
     doi = {10.1016/j.anihpb.2006.11.001},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2007__43_6_763_0}
}

Rodríguez Casal, Alberto. Set estimation under convexity type assumptions. Annales de l'I.H.P. Probabilités et statistiques, Tome 43 (2007) pp. 763-774. doi : 10.1016/j.anihpb.2006.11.001. http://gdmltest.u-ga.fr/item/AIHPB_2007__43_6_763_0/

[1] A. Baíllo, A. Cuevas, On the estimation of a star-shaped set, Adv. Appl. Probab. 33 (2001) 1-10. | MR 1875774 | Zbl 1003.62030

[2] A. Baíllo, A. Cuevas, A. Justel, Set estimation and nonparametric detection, Canad. J. Statist. 28 (2000) 765-782. | MR 1821433 | Zbl 1057.62026

[3] V. Bertholet, J.P. Rasson, S. Lissoir, About the automatic detection of training sets for multispectral images classification, in: Rizzi A., Vichi M., Bock H.H. (Eds.), Advances in Data Science and Classification, Springer, Berlin, 1988, pp. 221-226.

[4] A. Cuevas, M. Febrero, R. Fraiman, Cluster analysis: a further approach based on density estimation, Computational Statistics and Data Analysis 36 (2001) 441-459. | MR 1855727 | Zbl 1053.62537

[5] A. Cuevas, M. Febrero, R. Fraiman, Estimating the number of clusters, Canad. J. Statist. 28 (2000) 367-382. | MR 1792055 | Zbl 0981.62054

[6] A. Cuevas, R. Fraiman, A plug-in approach to support estimation, Ann. Statist. 25 (1997) 2300-2312. | MR 1604449 | Zbl 0897.62034

[7] A. Cuevas, A. Rodríguez-Casal, On boundary estimation, Adv. Appl. Probab. 36 (2004) 340-354. | MR 2058139 | Zbl 1045.62019

[8] L. Devroye, G.L. Wise, Detection of abnormal behavior via nonparametric estimation of the support, SIAM J. Appl. Math. 38 (1980) 480-488. | MR 579432 | Zbl 0479.62028

[9] L. Dümbgen, G. Walther, Rates of convergence for random approximations of convex sets, Adv. Appl. Probab. 28 (1996) 384-393. | MR 1387882 | Zbl 0861.60022

[10] G.A. Edgar, Measure, Topology and Fractal Geometry, Springer-Verlag, 1990. | MR 1065392 | Zbl 0727.28003

[11] H. Edelsbrunner, E.P. Mücke, Three dimensional alpha shapes, ACM Trans. Graph. 13 (1994) 43-72. | Zbl 0806.68107

[12] A.P. Korostelev, A.B. Tsybakov, Minimax Theory of Image Reconstruction, Springer-Verlag, 1993. | MR 1226450 | Zbl 0833.62039

[13] D. Marr, Vision, Freeman and Co, 1982.

[14] M. Rudemo, H. Stryhn, Approximating the distribution of maximum likelihood contour estimators in two-region images, Scand. J. Statist. 21 (1994) 41-55. | MR 1267042 | Zbl 0804.62044

[15] R. Schneider, Convex Bodies: The Brunn-Minkowski Theory, Cambridge University Press, 1993. | Zbl 0798.52001

[16] J. Serra, Image Analysis and Mathematical Morphology, Academic Press, 1982. | MR 753649 | Zbl 0565.92001

[17] A.B. Tsybakov, Optimal aggregation of classifiers in statistical learning, Ann. Statist. 1 (2004) 135-166. | MR 2051002 | Zbl 1105.62353

[18] G. Walther, Granulometric smoothing, Ann. Statist. 25 (1997) 2273-2299. | MR 1604445 | Zbl 0919.62026

[19] G. Walther, On a generalization of Blaschke's rolling theorem and the smoothing of surfaces, Math. Methods Appl. Sci. 22 (1999) 301-316. | MR 1671447 | Zbl 0933.52003

[20] W. Weil, J.A. Wieacker, Stochastic geometry, in: Handbook of Convex Geometry, vol. B, Elsevier, Amsterdam, 1993, pp. 1391-1438. | MR 1243013 | Zbl 0788.52002