Rolling-ball method for estimating the boundary of the support of a point-process intensity
Annales de l'I.H.P. Probabilités et statistiques, Volume 38 (2002) no. 6, p. 959-971
@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},
     publisher = {Elsevier},
     volume = {38},
     number = {6},
     year = {2002},
     pages = {959-971},
     zbl = {1011.62035},
     mrnumber = {1955346},
     language = {en},
     url = {http://www.numdam.org/item/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, Volume 38 (2002) no. 6, pp. 959-971. http://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. | MR 1292189 | Zbl 0808.60019

[2] A. Charnes, W.W. Cooper, A.Y. Lewin, L.M. Seiford, Data Envelope Analysis: Theory, Methodology and Applications, Kluwer, Boston, 1995. | Zbl 0858.00049

[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. | MR 207004 | Zbl 0138.41301

[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. | MR 1689226 | Zbl 1043.62105

[6] P. Groeneboom, Limit theorems for convex hulls, Probab. Theory Related Fields 79 (1988) 327-368. | MR 959514 | Zbl 0635.60012

[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. | MR 1648521 | Zbl 01211571

[9] W. Härdle, B.U. Park, A.B. Tsybakov, Estimation of non-sharp support boundaries, J. Multivariate Anal. 55 (1995) 205-218. | MR 1370400 | Zbl 0863.62030

[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 1666696

[11] A.P. Korostelev, A.B. Tsybakov, Minimax Theory of Image Reconstruction, Lecture Notes in Statistics, 82, Springer-Verlag, Berlin, 1993. | MR 1226450 | Zbl 0833.62039

[12] A.P. Korostelev, L. Simar, A.B. Tsybakov, Efficient estimation of monotone boundaries, Ann. Statist. 23 (1995) 476-489. | MR 1332577 | Zbl 0829.62043

[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. | MR 1744393 | Zbl 0817.62023

[14] E. Mammen, A.B. Tsybakov, Asymptotical minimax recovery of sets with smooth boundaries, Ann. Statist. 23 (1995) 502-524. | MR 1332579 | Zbl 0834.62038

[15] D.H. Mclain, Two dimensional interpolation from random data, Comput. J. 19 (1976) 178-181. | MR 431604 | Zbl 0321.65009

[16] J. Møller, Lectures on Random Voronoi Tessellations, Lecture Notes in Statistics, 87, Springer-Verlag, New York, 1994. | MR 1295245 | Zbl 0812.60016

[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. | MR 1341202 | Zbl 0829.60040

[18] B.D. Ripley, Spatial Statistics, Wiley, New York, 1981. | MR 624436 | Zbl 0583.62087

[19] J. O'Rourke, Computational Geometry in C, Cambridge University Press, Cambridge, 1994. | Zbl 0912.68201

[20] A. Rényi, R. Sulanke, On the convex hull of n randomly chosen points, Z. Wahrscheinlichkeitstheorie Verw. Geb. 2 (1963) 75-84. | Zbl 0118.13701

[21] A. Rényi, R. Sulanke, On the convex hull of n randomly chosen points II, Z. Wahrscheinlichkeitstheorie Verw. Geb. 3 (1964) 138-147. | MR 169139 | Zbl 0126.34103

[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.