On estimation of monotone and concave frontier functions
AbstractA way for measuring the efficiency of enterprises is via the estimation of the so-called production frontier, which is the upper boundary of the support of the population density in the input and output space. It is reasonable to assume that the production frontier is a concave monotone function. Then, a famous estimator is the data envelopment analysis (DEA) estimator, which is the lowest concave monotone increasing function covering all sample points. This estimator is biased downwards since it never exceeds the true production frontier. In this paper we derive the asymptotic distribution of the DEA estimator, which enables us to assess the asymptotic bias and hence to propose an improved bias corrected estimator. This bias corrected estimator involves consistent estimation of the density function as well as of the second derivative of the production frontier. We also discuss briefly the construction of asymptotic confidence intervals. The finite sample performance of the bias corrected estimator is investigated via a simulation study and the procedure is illustrated for a real data example.
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Bibliographic InfoPaper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers RP with number -1392.
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Note: In : Journal of the American Statistical Association, 94(445), 220-228, 1999
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- Gijbels, IrÃ¨ne & Mammen, Enno & Park, Byeong U. & Simar, LÃ©opold, 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, IrÃ¨ne & MAMMEN, Enno & PARK, Byeong U. & SIMAR, LÃ©opold, 1997. "On estimation of monotone and concave frontier functions," CORE Discussion Papers, UniversitÃ© catholique de Louvain, Center for Operations Research and Econometrics (CORE) 1997031, UniversitÃ© catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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