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

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  • Léopold Simar

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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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Bibliographic Info

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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Web page: http://www.springerlink.com/link.asp?id=100296

Related research

Keywords: Frontier; Nonparametric estimation; Stochastic DEA/FDH; Robustness to outliers; C13; C14; D20;

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References

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  1. Léopold Simar & Paul W. Wilson, 1998. "Sensitivity Analysis of Efficiency Scores: How to Bootstrap in Nonparametric Frontier Models," Management Science, INFORMS, vol. 44(1), pages 49-61, January.
  2. 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.
  3. 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).
  4. 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.
  5. Greene, William H., 1990. "A Gamma-distributed stochastic frontier model," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 141-163.
  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. Tsybakov, A.B. & Korostelev, A.P. & Simar, L., 1992. "Efficient Estimation of Monotone Boundaries," Papers 9209, Catholique de Louvain - Institut de statistique.
  8. 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.
  9. 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.
  10. O. B. Olesen & N. C. Petersen, 1995. "Chance Constrained Efficiency Evaluation," Management Science, INFORMS, vol. 41(3), pages 442-457, March.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. 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.
  17. 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.
  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, vol. 14(06), pages 783-793, December.
  19. Simar, L. & Wilson, P.W., 1998. "A General Methodology for Bootstrapping in Nonparametric Frontier Models," Papers 9811, Catholique de Louvain - Institut de statistique.
  20. Kneip, A. & Simar, L., . "A general framework for frontier estimation with panel data," CORE Discussion Papers RP -1224, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  21. Simar, L. & Wilson, P.W., 1999. "Statistical Inference in Nonparametric Frontier Models: the State of the Art," Papers 9904, Catholique de Louvain - Institut de statistique.
  22. Daouia, Abdelaati & Simar, Leopold, 2007. "Nonparametric efficiency analysis: A multivariate conditional quantile approach," Journal of Econometrics, Elsevier, vol. 140(2), pages 375-400, October.
  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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Citations

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Cited by:
  1. Zervopoulos, Panagiotis, 2012. "Dealing with small samples and dimensionality issues in data envelopment analysis," MPRA Paper 39226, University Library of Munich, Germany.
  2. Wolfgang Härdle & Seok-Oh Jeong, 2005. "Nonparametric Productivity Analysis," SFB 649 Discussion Papers SFB649DP2005-013, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  3. 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, vol. 49(C), pages 220-231.
  4. Anne-Kathrin Last & Heike Wetzel, 2009. "Effizienzmessverfahren – eine Einführung," Working Paper Series in Economics 145, University of Lüneburg, Institute of Economics.
  5. Leopold Simar & Valentin Zelenyuk, 2008. "Stochastic FDH/DEA estimators for Frontier Analysis," Discussion Papers 8, Kyiv School of Economics.
  6. Dongwei Su & Xingxing He, 2012. "Ownership structure, corporate governance and productive efficiency in China," Journal of Productivity Analysis, Springer, vol. 38(3), pages 303-318, December.
  7. Timo Kuosmanen & Mika Kortelainen, 2012. "Stochastic non-smooth envelopment of data: semi-parametric frontier estimation subject to shape constraints," Journal of Productivity Analysis, Springer, vol. 38(1), pages 11-28, August.
  8. Badin, Luiza & Daraio, Cinzia & Simar, Léopold, 2010. "Optimal bandwidth selection for conditional efficiency measures: A data-driven approach," European Journal of Operational Research, Elsevier, vol. 201(2), pages 633-640, March.
  9. 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.
  10. 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, vol. 27(1), pages 55-73, January.
  11. Vitaliy Zheka, 2006. "Corporate Governance and Firm Performance in Ukraine," CERT Discussion Papers 0605, Centre for Economic Reform and Transformation, Heriot Watt University.
  12. Uwe Cantner & Jens J. Krüger & Rene Söllner, 2010. "Product Quality, Product Price, and Share Dynamics in the German Compact Car Market," Jena Economic Research Papers 2010-024, Friedrich-Schiller-University Jena, Max-Planck-Institute of Economics.
  13. 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.
  14. Udhayakumar, A. & Charles, V. & Kumar, Mukesh, 2011. "Stochastic simulation based genetic algorithm for chance constrained data envelopment analysis problems," Omega, Elsevier, vol. 39(4), pages 387-397, August.
  15. 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 96827, New Zealand Agricultural and Resource Economics Society.

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