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On estimation of monotone and concave frontier functions

  • GIJBELS, Irène

    (Institut de Statistique, Université catholique de Louvain, Louvain-la-Neuve, Belgium)

  • MAMMEN, Enno

    (Institut für Angewandte Mathematik, Universität Heidelberg)

  • PARK, Byeong U.

    (Department of Statistics, Seoul National University, North Korea)

  • SIMAR, Léopold

    ()

    (Center for Operations Research and Econometrics (CORE), Université catholique de Louvain (UCL), Louvain la Neuve, Belgium)

A 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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Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 1997031.

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Date of creation: 01 Apr 1997
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Handle: RePEc:cor:louvco:1997031
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  1. Greene, William H., 1990. "A Gamma-distributed stochastic frontier model," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 141-163.
  2. 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.
  3. Christensen, Laurits R & Greene, William H, 1976. "Economies of Scale in U.S. Electric Power Generation," Journal of Political Economy, University of Chicago Press, vol. 84(4), pages 655-76, August.
  4. Greene, William H., 1980. "Maximum likelihood estimation of econometric frontier functions," Journal of Econometrics, Elsevier, vol. 13(1), pages 27-56, May.
  5. Berndt, Ernst R. & Christensen, Laurits R., 1973. "The translog function and the substitution of equipment, structures, and labor in U.S. manufacturing 1929-68," Journal of Econometrics, Elsevier, vol. 1(1), pages 81-113, March.
  6. Rajiv D. Banker, 1993. "Maximum Likelihood, Consistency and Data Envelopment Analysis: A Statistical Foundation," Management Science, INFORMS, vol. 39(10), pages 1265-1273, October.
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