no. 6
Rolling-ball method for estimating the boundary of the support of a point-process intensity
Hall, Peter1 ; Park, Byeong U. ; Turlach, Berwin A.
1 Australian National University, centre for Mathematics and its Applications, Mathematical Sciences Institute, John Dedman Building, Canberra ACT 0200 (AUSTRALIE)
Annales de l'I.H.P. Probabilités et statistiques, Tome 38 (2002) no. 6, pp. 959-971

Hall, Peter 1 ; Park, Byeong U.  ; Turlach, Berwin A. 

1 Australian National University, centre for Mathematics and its Applications, Mathematical Sciences Institute, John Dedman Building, Canberra ACT 0200 (AUSTRALIE) 
@article{AIHPB_2002__38_6_959_0,
     author = {Hall, Peter and Park, Byeong U. and Turlach, Berwin A.},
     title = {Rolling-ball method for estimating the boundary of the support of a point-process intensity},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {959--971},
     year = {2002},
     publisher = {Elsevier},
     volume = {38},
     number = {6},
     mrnumber = {1955346},
     zbl = {1011.62035},
     language = {en},
     url = {https://www.numdam.org/item/AIHPB_2002__38_6_959_0/}
}
TY  - JOUR
AU  - Hall, Peter
AU  - Park, Byeong U.
AU  - Turlach, Berwin A.
TI  - Rolling-ball method for estimating the boundary of the support of a point-process intensity
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 2002
SP  - 959
EP  - 971
VL  - 38
IS  - 6
PB  - Elsevier
UR  - https://www.numdam.org/item/AIHPB_2002__38_6_959_0/
LA  - en
ID  - AIHPB_2002__38_6_959_0
ER  - 
%0 Journal Article
%A Hall, Peter
%A Park, Byeong U.
%A Turlach, Berwin A.
%T Rolling-ball method for estimating the boundary of the support of a point-process intensity
%J Annales de l'I.H.P. Probabilités et statistiques
%D 2002
%P 959-971
%V 38
%N 6
%I Elsevier
%U https://www.numdam.org/item/AIHPB_2002__38_6_959_0/
%G en
%F AIHPB_2002__38_6_959_0
Hall, Peter; Park, Byeong U.; Turlach, Berwin A. Rolling-ball method for estimating the boundary of the support of a point-process intensity. Annales de l'I.H.P. Probabilités et statistiques, Tome 38 (2002) no. 6, pp. 959-971. https://www.numdam.org/item/AIHPB_2002__38_6_959_0/

[1] A.J. Cabo, P. Groeneboom, Limit theorems for functionals of convex hulls, Probab. Theory Related Fields 100 (1994) 31-55. | Zbl | MR

[2] A. Charnes, W.W. Cooper, A.Y. Lewin, L.M. Seiford, Data Envelope Analysis: Theory, Methodology and Applications, Kluwer, Boston, 1995. | Zbl

[3] L. Christensen, R. Greene, Economics of scale in US electric power generation, J. Polit. Economy 84 (1976) 653-667.

[4] B. Efron, The convex hull of a random set of points, Biometrika 52 (1965) 331-343. | Zbl | MR

[5] I. Gijbels, E. Mammen, B.U. Park, L. Simar, On estimation of monotone and concave frontier functions, J. Amer. Statist. Assoc. 94 (1999) 220-228. | Zbl | MR

[6] P. Groeneboom, Limit theorems for convex hulls, Probab. Theory Related Fields 79 (1988) 327-368. | Zbl | MR

[7] S. Grosskopf, Statistical inference and nonparametric efficiency: a selective survey, J. Productivity Anal. 7 (1996) 161-176.

[8] P. Hall, B.U. Park, S. Stern, On polynomial estimators of frontiers and boundaries, J. Multivariate Anal. 66 (1998) 71-98. | Zbl | MR

[9] W. Härdle, B.U. Park, A.B. Tsybakov, Estimation of non-sharp support boundaries, J. Multivariate Anal. 55 (1995) 205-218. | Zbl | MR

[10] A. Kneip, B.U. Park, L. Simar, A note on the convergence of nonparametric DEA estimators for production efficiency scores, Econometric Theory 14 (1998) 783-793. | MR

[11] A.P. Korostelev, A.B. Tsybakov, Minimax Theory of Image Reconstruction, Lecture Notes in Statistics, 82, Springer-Verlag, Berlin, 1993. | Zbl | MR

[12] A.P. Korostelev, L. Simar, A.B. Tsybakov, Efficient estimation of monotone boundaries, Ann. Statist. 23 (1995) 476-489. | Zbl | MR

[13] A.P. Korostelev, L. Simar, A.B. Tsybakov, On estimation of monotone and convex boundaries, Pub. Inst. Statist. Univ. Paris 49 (1995) 3-18. | Zbl | MR

[14] E. Mammen, A.B. Tsybakov, Asymptotical minimax recovery of sets with smooth boundaries, Ann. Statist. 23 (1995) 502-524. | Zbl | MR

[15] D.H. Mclain, Two dimensional interpolation from random data, Comput. J. 19 (1976) 178-181. | Zbl | MR

[16] J. Møller, Lectures on Random Voronoi Tessellations, Lecture Notes in Statistics, 87, Springer-Verlag, New York, 1994. | Zbl | MR

[17] A.V. Nagaev, Some properties of convex hulls generated by homogeneous Poisson point processes in an unbounded convex domain, Ann. Inst. Statist. Math. 47 (1995) 21-29. | Zbl | MR

[18] B.D. Ripley, Spatial Statistics, Wiley, New York, 1981. | Zbl | MR

[19] J. O'Rourke, Computational Geometry in C, Cambridge University Press, Cambridge, 1994. | Zbl

[20] A. Rényi, R. Sulanke, On the convex hull of n randomly chosen points, Z. Wahrscheinlichkeitstheorie Verw. Geb. 2 (1963) 75-84. | Zbl

[21] A. Rényi, R. Sulanke, On the convex hull of n randomly chosen points II, Z. Wahrscheinlichkeitstheorie Verw. Geb. 3 (1964) 138-147. | Zbl | MR

[22] L.M. Seiford, Data envelopment analysis: the evolution of the state-of-the-art, 1978-1995, J. Productivity Anal. 7 (1996) 99-137.

[23] R. Turner, D. Macqueen, S function Deldir to compute the Dirichlet (Voronoi) tesselation and Delaunay triangulation of a planar set of data points, Available from Statlib, 1996.