Limit Distribution of Convex-Hull Estimators of Boundaries
Given n independent and identically distributed observations in a set G with an unknown function g, called a boundary or frontier, it is desired to estimate g from the observations. The problem has several important applications including classification and cluster analysis, and is closely related to edge estimation in image reconstruction. It is particularly important in econometrics. The convex-hull estimator of a boundary or frontier is very popular in econometrics, where it is a cornerstone of a method known as `data envelope analysis´ or DEA. In this paper we give a large sample approximation of the distribution of the convex-hull estimator in the general case where p>=1. We discuss ways of using the large sample approximation to correct the bias of the convex-hull and the DEA estimators and to construct confidence intervals for the true function.
|Date of creation:||2004|
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- Léopold Simar & Paul Wilson, 2000.
"Statistical Inference in Nonparametric Frontier Models: The State of the Art,"
Journal of Productivity Analysis,
Springer, vol. 13(1), pages 49-78, January.
- Simar, L. & Wilson, P.W., 1999. "Statistical Inference in Nonparametric Frontier Models: the State of the Art," Papers 9904, Catholique de Louvain - Institut de statistique.
- Kneip, Alois & Park, Byeong U. & Simar, L opold, 1998. "A Note On The Convergence Of Nonparametric Dea Estimators For Production Efficiency Scores," Econometric Theory, Cambridge University Press, vol. 14(06), pages 783-793, December.
- Hall, Peter & Park, Byeong U. & Stern, Steven E., 1998. "On Polynomial Estimators of Frontiers and Boundaries," Journal of Multivariate Analysis, Elsevier, vol. 66(1), pages 71-98, July.
- Hardle, W. & Park, B. U. & Tsybakov, A. B., 1995. "Estimation of Non-sharp Support Boundaries," Journal of Multivariate Analysis, Elsevier, vol. 55(2), pages 205-218, November.
- GIJBELS, Irène & MAMMEN, Enno & PARK, Byeong U. & SIMAR, Léopold, .
"On estimation of monotone and concave frontier functions,"
CORE Discussion Papers RP
1392, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Gijbels, Irène & Mammen, Enno & Park, Byeong U. & Simar, Léopold, 1998. "On estimation of monotone and concave frontier functions," SFB 373 Discussion Papers 1998,9, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- GIJBELS, Irène & MAMMEN, Enno & PARK, Byeong U. & SIMAR, Léopold, 1997. "On estimation of monotone and concave frontier functions," CORE Discussion Papers 1997031, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Tsybakov, A.B. & Korostelev, A.P. & Simar, L., 1992. "Efficient Estimation of Monotone Boundaries," Papers 9209, Catholique de Louvain - Institut de statistique.
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