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How to improve the performances of DEA/FDH estimators in the presence of noise?

  • Léopold Simar

    ()

In frontier analysis, most of the nonparametric approaches (DEA, FDH) are based on envelopment ideas which suppose that with probability one, all the observed units belong to the attainable set. In these "deterministic" frontier models, statistical theory is now mostly available. In the presence of noise, this is no more true and envelopment estimators could behave dramatically since they are very sensitive to extreme observations that could result only from noise. DEA/FDH techniques would provide estimators with an error of the order of the standard deviation of the noise. In this paper we propose to adapt some recent results on detecting change points, to improve the performances of the classical DEA/FDH estimators in the presence of noise. We show by simulated examples that the procedure works well when the noise is of moderate size, in term of noise to signal ratio. It turns out that the procedure is also robust to outliers.

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File URL: http://hdl.handle.net/10.1007/s11123-007-0057-3
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Article provided by Springer in its journal Journal of Productivity Analysis.

Volume (Year): 28 (2007)
Issue (Month): 3 (December)
Pages: 183-201

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Handle: RePEc:kap:jproda:v:28:y:2007:i:3:p:183-201
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  1. Atkinson, Scott E. & Primont, Daniel, 2002. "Stochastic estimation of firm technology, inefficiency, and productivity growth using shadow cost and distance functions," Journal of Econometrics, Elsevier, vol. 108(2), pages 203-225, June.
  2. Jondrow, James & Knox Lovell, C. A. & Materov, Ivan S. & Schmidt, Peter, 1982. "On the estimation of technical inefficiency in the stochastic frontier production function model," Journal of Econometrics, Elsevier, vol. 19(2-3), pages 233-238, August.
  3. Racine, Jeff & Li, Qi, 2004. "Nonparametric estimation of regression functions with both categorical and continuous data," Journal of Econometrics, Elsevier, vol. 119(1), pages 99-130, March.
  4. Simar, L. & Wilson, P.W., . "Sensitivity analysis of efficiency scores: how to bootstrap in nonparametric frontier models," CORE Discussion Papers RP -1304, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Shawna Grosskopf & Kathy J. Hayes & Lori L. Taylor & William L. Weber, 1997. "Budget-Constrained Frontier Measures Of Fiscal Equality And Efficiency In Schooling," The Review of Economics and Statistics, MIT Press, vol. 79(1), pages 116-124, February.
  6. Leopold Simar & Paul Wilson, 2010. "Inferences from Cross-Sectional, Stochastic Frontier Models," Econometric Reviews, Taylor & Francis Journals, vol. 29(1), pages 62-98.
  7. 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).
  8. Park, B.U. & Simar, L. & Weiner, Ch., 2000. "The Fdh Estimator For Productivity Efficiency Scores," Econometric Theory, Cambridge University Press, vol. 16(06), pages 855-877, December.
  9. Cazals, Catherine & Florens, Jean-Pierre & Simar, Leopold, 2002. "Nonparametric frontier estimation: a robust approach," Journal of Econometrics, Elsevier, vol. 106(1), pages 1-25, January.
  10. Kumbhakar, Subal C. & Park, Byeong U. & Simar, Leopold & Tsionas, Efthymios G., 2007. "Nonparametric stochastic frontiers: A local maximum likelihood approach," Journal of Econometrics, Elsevier, vol. 137(1), pages 1-27, March.
  11. Aigner, Dennis & Lovell, C. A. Knox & Schmidt, Peter, 1977. "Formulation and estimation of stochastic frontier production function models," Journal of Econometrics, Elsevier, vol. 6(1), pages 21-37, July.
  12. 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.
  13. 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.
  14. Daouia, Abdelaati & Simar, Leopold, 2007. "Nonparametric efficiency analysis: A multivariate conditional quantile approach," Journal of Econometrics, Elsevier, vol. 140(2), pages 375-400, October.
  15. A. Charnes & W. W. Cooper & E. Rhodes, 1981. "Evaluating Program and Managerial Efficiency: An Application of Data Envelopment Analysis to Program Follow Through," Management Science, INFORMS, vol. 27(6), pages 668-697, June.
  16. KNEIP, Alois & SIMAR, Léopold, 1995. "A General Framework for Frontier Estimation with Panel Data," CORE Discussion Papers 1995060, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  17. Leopold Simar & Paul Wilson, 2000. "A general methodology for bootstrapping in non-parametric frontier models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(6), pages 779-802.
  18. O. B. Olesen & N. C. Petersen, 1995. "Chance Constrained Efficiency Evaluation," Management Science, INFORMS, vol. 41(3), pages 442-457, March.
  19. Cinzia Daraio & Léopold Simar, 2005. "Introducing Environmental Variables in Nonparametric Frontier Models: a Probabilistic Approach," Journal of Productivity Analysis, Springer, vol. 24(1), pages 93-121, 09.
  20. Greene, William H., 1990. "A Gamma-distributed stochastic frontier model," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 141-163.
  21. Tsybakov, A.B. & Korostelev, A.P. & Simar, L., 1992. "Efficient Estimation of Monotone Boundaries," Papers 9209, Catholique de Louvain - Institut de statistique.
  22. Jeong, Seok-Oh & Simar, Léopold, 2006. "Linearly interpolated FDH efficiency score for nonconvex frontiers," Journal of Multivariate Analysis, Elsevier, vol. 97(10), pages 2141-2161, November.
  23. 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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