Rolling-ball method for estimating the boundary of the support of a point-process intensity
Peter Hall[1]; Byeong U. Park; Berwin A. Turlach
- [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 (2002)
- Volume: 38, Issue: 6, page 959-971
- ISSN: 0246-0203
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topHall, Peter, Park, Byeong U., and 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 38.6 (2002): 959-971. <http://eudml.org/doc/77750>.
@article{Hall2002,
affiliation = {Australian National University, centre for Mathematics and its Applications, Mathematical Sciences Institute, John Dedman Building, Canberra ACT 0200 (AUSTRALIE)},
author = {Hall, Peter, Park, Byeong U., Turlach, Berwin A.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {bias correction; confidence band; curvature; envelope; frontier; productivity analysis; rotation invariance},
language = {eng},
number = {6},
pages = {959-971},
publisher = {Elsevier},
title = {Rolling-ball method for estimating the boundary of the support of a point-process intensity},
url = {http://eudml.org/doc/77750},
volume = {38},
year = {2002},
}
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
PB - Elsevier
VL - 38
IS - 6
SP - 959
EP - 971
LA - eng
KW - bias correction; confidence band; curvature; envelope; frontier; productivity analysis; rotation invariance
UR - http://eudml.org/doc/77750
ER -
References
top- [1] A.J. Cabo, P. Groeneboom, Limit theorems for functionals of convex hulls, Probab. Theory Related Fields100 (1994) 31-55. Zbl0808.60019MR1292189
- [2] A. Charnes, W.W. Cooper, A.Y. Lewin, L.M. Seiford, Data Envelope Analysis: Theory, Methodology and Applications, Kluwer, Boston, 1995. Zbl0858.00049
- [3] L. Christensen, R. Greene, Economics of scale in US electric power generation, J. Polit. Economy84 (1976) 653-667.
- [4] B. Efron, The convex hull of a random set of points, Biometrika52 (1965) 331-343. Zbl0138.41301MR207004
- [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. Zbl1043.62105MR1689226
- [6] P. Groeneboom, Limit theorems for convex hulls, Probab. Theory Related Fields79 (1988) 327-368. Zbl0635.60012MR959514
- [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. Zbl1127.62358MR1648521
- [9] W. Härdle, B.U. Park, A.B. Tsybakov, Estimation of non-sharp support boundaries, J. Multivariate Anal.55 (1995) 205-218. Zbl0863.62030MR1370400
- [10] A. Kneip, B.U. Park, L. Simar, A note on the convergence of nonparametric DEA estimators for production efficiency scores, Econometric Theory14 (1998) 783-793. MR1666696
- [11] A.P. Korostelev, A.B. Tsybakov, Minimax Theory of Image Reconstruction, Lecture Notes in Statistics, 82, Springer-Verlag, Berlin, 1993. Zbl0833.62039MR1226450
- [12] A.P. Korostelev, L. Simar, A.B. Tsybakov, Efficient estimation of monotone boundaries, Ann. Statist.23 (1995) 476-489. Zbl0829.62043MR1332577
- [13] A.P. Korostelev, L. Simar, A.B. Tsybakov, On estimation of monotone and convex boundaries, Pub. Inst. Statist. Univ. Paris49 (1995) 3-18. Zbl0817.62023MR1744393
- [14] E. Mammen, A.B. Tsybakov, Asymptotical minimax recovery of sets with smooth boundaries, Ann. Statist.23 (1995) 502-524. Zbl0834.62038MR1332579
- [15] D.H. McLain, Two dimensional interpolation from random data, Comput. J.19 (1976) 178-181. Zbl0321.65009MR431604
- [16] J. Møller, Lectures on Random Voronoi Tessellations, Lecture Notes in Statistics, 87, Springer-Verlag, New York, 1994. Zbl0812.60016MR1295245
- [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. Zbl0829.60040MR1341202
- [18] B.D. Ripley, Spatial Statistics, Wiley, New York, 1981. Zbl0583.62087MR624436
- [19] J. O'Rourke, Computational Geometry in C, Cambridge University Press, Cambridge, 1994. Zbl0912.68201
- [20] A. Rényi, R. Sulanke, On the convex hull of n randomly chosen points, Z. Wahrscheinlichkeitstheorie Verw. Geb.2 (1963) 75-84. Zbl0118.13701
- [21] A. Rényi, R. Sulanke, On the convex hull of n randomly chosen points II, Z. Wahrscheinlichkeitstheorie Verw. Geb.3 (1964) 138-147. Zbl0126.34103MR169139
- [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.
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