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Nonparametric frontier estimation: A robust approach. (English) Zbl 1051.62116

Summary: Most nonparametric methods for estimating production frontiers (data envelopment analysis and free disposal hull (FDH)) are based on envelopment techniques. Statistical inference based on these estimators is available but, by construction, they are very sensitive to extreme values or outliers. We propose a nonparametric estimator, which is more robust to these extreme values. It is based on a concept of expected minimum input function (or expected maximal output function). We show how this function is related to the efficient frontier itself. The resulting estimator is related to the FDH estimator but it will not envelop all the data. The asymptotic theory is provided. Our approach includes the multiple input and multiple output cases.

MSC:

62P20 Applications of statistics to economics
62G05 Nonparametric estimation
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[1] Aigner, D. J.; Lovell, C. A. K.; Schmidt, P.: Formulation and estimation of stochastic frontier models. Journal of econometrics 6, 21-37 (1977) · Zbl 0366.90026
[2] Aït-Sahalia, Y., 1995. The Delta Method for Nonlinear Kernel Functionals. Working paper, University of Chicago.
[3] Cazals, C., Florens, J.P., 1997. The Expected Minimum Cost Function: A Nonparametric Approach. Working paper, IDEI, University of Toulouse.
[4] Charnes, A.; Cooper, W. W.; Rhodes, E.: Measuring the inefficiency of decision making units. European journal of operational research 2, 429-444 (1978) · Zbl 0416.90080
[5] Debreu, G.: The coefficient of resource utilization. Econometrica 19, No. 3, 273-292 (1951) · Zbl 0045.41404
[6] Deprins, D., Simar, L., Tulkens, H., 1984. Measuring labor inefficiency in post offices. In: Marchand, M., Pestieau, P., Tulkens, H. (Eds.), The Performance of Public Enterprises: Concepts and Measurements. Amsterdam, North-Holland, pp. 243–267.
[7] Farrell, M. J.: The measurement of productive efficiency. Journal of the royal statistical society series A 120, 253-281 (1957)
[8] Kneip, A.; Park, B. U.; Simar, L.: A note on the convergence of nonparametric DEA estimators for production efficiency scores. Econometric theory 14, 783-793 (1998)
[9] Koopmans, T. C.: An analysis of production as an efficient combination of activities.. Activity analysis of production and allocation. Cowles commission for research in economics monograph 13. (1951) · Zbl 0045.09506
[10] Meeusen, W.; Den Broek, J. Van: Efficiency estimation from cobb–Douglas production function with composed error. International economic review 8, 435-444 (1977) · Zbl 0366.90025
[11] Park, B.; Simar, L.; Weiner, Ch.: The FDH estimator for productivity efficiency scores: asymptotic properties. Econometric theory 16, 855-877 (2000) · Zbl 0967.62102
[12] Seiford, L. M.: Data envelopment analysis: the evolution of the state-of-the-art (1978–1995). Journal of productivity analysis 7, 99-137 (1996)
[13] Serfling, R. T.: Approximation of mathematical statistics.. (1980) · Zbl 0538.62002
[14] Shephard, R. W.: Theory of cost and production function.. (1970) · Zbl 0244.90011
[15] Simar, L.; Wilson, P. W.: Statistical inference in nonparametric frontier models: the state of the art. Journal of productivity analysis 13, 49-78 (2000)
[16] Van Der Vaard, A.; Wellner, J. A.: Weak convergence and empirical processes.. (1996)
[17] Wilson, P. W.: Detecting outliers in deterministic nonparametric frontier models with multiple outputs. Journal of business and economic statistics 11, 319-323 (1993)
[18] Wilson, P. W.: Detecting influential observations in data envelopment analysis. Journal of productivity analysis 6, 27-45 (1995)
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