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How to Improve the Performances of DEA/FDH Estimators in the Presence of Noise?

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  • Simar, Léopold

Abstract

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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Paper provided by Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes in its series SFB 373 Discussion Papers with number 2003,33.

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Date of creation: 2003
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Handle: RePEc:zbw:sfb373:200333

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Keywords: Nonparametric frontier; Stochastic DEA/FDH; Robustness to outliers;

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References

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  1. Daouia, Abdelaati & Simar, Leopold, 2007. "Nonparametric efficiency analysis: A multivariate conditional quantile approach," Journal of Econometrics, Elsevier, Elsevier, vol. 140(2), pages 375-400, October.
  2. Simar, L. & Wilson, P.W., 1998. "A General Methodology for Bootstrapping in Nonparametric Frontier Models," Papers, Catholique de Louvain - Institut de statistique 9811, Catholique de Louvain - Institut de statistique.
  3. Tsybakov, A.B. & Korostelev, A.P. & Simar, L., 1992. "Efficient Estimation of Monotone Boundaries," Papers, Catholique de Louvain - Institut de statistique 9209, Catholique de Louvain - Institut de statistique.
  4. 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, INFORMS, vol. 27(6), pages 668-697, June.
  5. GIJBELS, Irène & MAMMEN, Enno & PARK, Byeong U. & SIMAR, Léopold, . "On estimation of monotone and concave frontier functions," CORE Discussion Papers RP, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) -1392, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  6. Aigner, Dennis & Lovell, C. A. Knox & Schmidt, Peter, 1977. "Formulation and estimation of stochastic frontier production function models," Journal of Econometrics, Elsevier, Elsevier, vol. 6(1), pages 21-37, July.
  7. Cazals, Catherine & Florens, Jean-Pierre & Simar, Leopold, 2002. "Nonparametric frontier estimation: a robust approach," Journal of Econometrics, Elsevier, Elsevier, vol. 106(1), pages 1-25, January.
  8. Greene, William H., 1990. "A Gamma-distributed stochastic frontier model," Journal of Econometrics, Elsevier, Elsevier, vol. 46(1-2), pages 141-163.
  9. Léopold Simar & Paul Wilson, 2000. "Statistical Inference in Nonparametric Frontier Models: The State of the Art," Journal of Productivity Analysis, Springer, Springer, vol. 13(1), pages 49-78, January.
  10. O. B. Olesen & N. C. Petersen, 1995. "Chance Constrained Efficiency Evaluation," Management Science, INFORMS, INFORMS, vol. 41(3), pages 442-457, March.
  11. Cinzia Daraio & Léopold Simar, 2005. "Introducing Environmental Variables in Nonparametric Frontier Models: a Probabilistic Approach," Journal of Productivity Analysis, Springer, Springer, vol. 24(1), pages 93-121, 09.
  12. Kumbhakar, Subal C. & Park, Byeong U. & Simar, Leopold & Tsionas, Efthymios G., 2007. "Nonparametric stochastic frontiers: A local maximum likelihood approach," Journal of Econometrics, Elsevier, Elsevier, vol. 137(1), pages 1-27, March.
  13. Jeong, Seok-Oh & Simar, Léopold, 2006. "Linearly interpolated FDH efficiency score for nonconvex frontiers," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 97(10), pages 2141-2161, November.
  14. Rajiv D. Banker, 1993. "Maximum Likelihood, Consistency and Data Envelopment Analysis: A Statistical Foundation," Management Science, INFORMS, INFORMS, vol. 39(10), pages 1265-1273, October.
  15. Kneip, A. & Simar, L., . "A general framework for frontier estimation with panel data," CORE Discussion Papers RP, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) -1224, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  16. Léopold Simar & Paul W. Wilson, 1998. "Sensitivity Analysis of Efficiency Scores: How to Bootstrap in Nonparametric Frontier Models," Management Science, INFORMS, INFORMS, vol. 44(1), pages 49-61, January.
  17. Racine, Jeff & Li, Qi, 2004. "Nonparametric estimation of regression functions with both categorical and continuous data," Journal of Econometrics, Elsevier, Elsevier, vol. 119(1), pages 99-130, March.
  18. 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, Cambridge University Press, vol. 14(06), pages 783-793, December.
  19. Leopold Simar & Paul Wilson, 2010. "Inferences from Cross-Sectional, Stochastic Frontier Models," Econometric Reviews, Taylor & Francis Journals, Taylor & Francis Journals, vol. 29(1), pages 62-98.
  20. 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, Elsevier, vol. 19(2-3), pages 233-238, August.
  21. 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.
  22. Park, B.U. & Simar, L. & Weiner, Ch., 2000. "The Fdh Estimator For Productivity Efficiency Scores," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 16(06), pages 855-877, December.
  23. 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, Elsevier, vol. 108(2), pages 203-225, June.
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Citations

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Cited by:
  1. Wolfgang Härdle & Seok-Oh Jeong, 2005. "Nonparametric Productivity Analysis," SFB 649 Discussion Papers SFB649DP2005-013, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  2. Anne-Kathrin Last & Heike Wetzel, 2009. "Effizienzmessverfahren – eine Einführung," Working Paper Series in Economics, University of Lüneburg, Institute of Economics 145, University of Lüneburg, Institute of Economics.
  3. Leopold Simar & Valentin Zelenyuk, 2008. "Stochastic FDH/DEA estimators for Frontier Analysis," Discussion Papers 8, Kyiv School of Economics.
  4. Zervopoulos, Panagiotis, 2012. "Dealing with small samples and dimensionality issues in data envelopment analysis," MPRA Paper 39226, University Library of Munich, Germany.
  5. Dongwei Su & Xingxing He, 2012. "Ownership structure, corporate governance and productive efficiency in China," Journal of Productivity Analysis, Springer, Springer, vol. 38(3), pages 303-318, December.
  6. Filippou, Miltiades & Zervopoulos, Panagiotis, 2011. "Developing a hybrid comparative optimization model for short-term forecasting: an ‘idle time interval’ roadmap for operational units’ strategic planning," MPRA Paper 41573, University Library of Munich, Germany.
  7. Vitaliy Zheka, 2006. "Corporate Governance and Firm Performance in Ukraine," CERT Discussion Papers, Centre for Economic Reform and Transformation, Heriot Watt University 0605, Centre for Economic Reform and Transformation, Heriot Watt University.
  8. Prakashan Veettil & Stijn Speelman & Guido Huylenbroeck, 2013. "Estimating the Impact of Water Pricing on Water Use Efficiency in Semi-arid Cropping System: An Application of Probabilistically Constrained Nonparametric Efficiency Analysis," Water Resources Management, Springer, Springer, vol. 27(1), pages 55-73, January.
  9. Ortega Irizo, Fco. Javier & Basulto Santos, Jesús, 2009. "Estimación Bayesiana en modelos de producción con frontera determinista/Bayesian Estimation in Deterministic Frontier Production Models," Estudios de Economía Aplicada, Estudios de Economía Aplicada, vol. 27, pages 573 (22 Pá, Agosto.
  10. Uwe Cantner & Jens J. Krüger & René Söllner, 2012. "Product quality, product price, and share dynamics in the German compact car market," Industrial and Corporate Change, Oxford University Press, vol. 21(5), pages 1085-1115, October.
  11. Yuen, Andrew Chi-lok & Zhang, Anming & Cheung, Waiman, 2013. "Foreign participation and competition: A way to improve the container port efficiency in China?," Transportation Research Part A: Policy and Practice, Elsevier, Elsevier, vol. 49(C), pages 220-231.
  12. Timo Kuosmanen & Mika Kortelainen, 2012. "Stochastic non-smooth envelopment of data: semi-parametric frontier estimation subject to shape constraints," Journal of Productivity Analysis, Springer, Springer, vol. 38(1), pages 11-28, August.
  13. Chand, Narendra & Kerr, Geoffrey N. & Bigsby, Hugh R., . "Why some community forests are performing better than others: a case of forest user groups in Nepal," 2010 Conference, August 26-27, 2010, Nelson, New Zealand, New Zealand Agricultural and Resource Economics Society 96827, New Zealand Agricultural and Resource Economics Society.
  14. Badin, Luiza & Daraio, Cinzia & Simar, Léopold, 2010. "Optimal bandwidth selection for conditional efficiency measures: A data-driven approach," European Journal of Operational Research, Elsevier, Elsevier, vol. 201(2), pages 633-640, March.
  15. Udhayakumar, A. & Charles, V. & Kumar, Mukesh, 2011. "Stochastic simulation based genetic algorithm for chance constrained data envelopment analysis problems," Omega, Elsevier, Elsevier, vol. 39(4), pages 387-397, August.

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