no. 6
Set estimation under convexity type assumptions
Annales de l'I.H.P. Probabilités et statistiques, Tome 43 (2007) no. 6, pp. 763-774 
@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},
     pages = {763--774},
     year = {2007},
     publisher = {Elsevier},
     volume = {43},
     number = {6},
     doi = {10.1016/j.anihpb.2006.11.001},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.anihpb.2006.11.001/}
}
TY  - JOUR
AU  - Rodríguez Casal, Alberto
TI  - Set estimation under convexity type assumptions
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 2007
SP  - 763
EP  - 774
VL  - 43
IS  - 6
PB  - Elsevier
UR  - https://www.numdam.org/articles/10.1016/j.anihpb.2006.11.001/
DO  - 10.1016/j.anihpb.2006.11.001
LA  - en
ID  - AIHPB_2007__43_6_763_0
ER  - 
%0 Journal Article
%A Rodríguez Casal, Alberto
%T Set estimation under convexity type assumptions
%J Annales de l'I.H.P. Probabilités et statistiques
%D 2007
%P 763-774
%V 43
%N 6
%I Elsevier
%U https://www.numdam.org/articles/10.1016/j.anihpb.2006.11.001/
%R 10.1016/j.anihpb.2006.11.001
%G en
%F 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) no. 6, pp. 763-774. doi: 10.1016/j.anihpb.2006.11.001

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

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

[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. | Zbl | MR

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

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

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

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

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

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

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

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

[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. | Zbl | MR

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

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

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

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

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

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

Cité par Sources :