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Aspects of Statistical Analysis in DEA-Type Frontier Models

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  • SIMAR , Léopold

    (CORE and Institut de Statistique, Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium)

Abstract

In Grosskopf (1995) and Banker (1995) different approaches and problems of statistical inference in DEA frontier models are presented. This paper focuses on the basic characteristics of DEA models from a statistical point of view. It arose from comments and discussions on both papers above. The framework of DEA models is deterministic (all the observed points lie on the same side of the frontier) nevertheless a stochastic statistical model can be constructed once a data generating process is defined. So statistical analysis may be performed and sampling properties of DEA estimators can be established. However, practical statistical inference (like test of hypothesis, confidence intervals, ... ) still needs artifacts like the bootstrap to be performed. A consistent bootstrap relies also on a clear definition of the data generating process and on a consistent estimator of it: the approach of Simar and Wilson (1995) is described. Finally, some trails are proposed for introducing stochastic noise in DEA models, in the spirit of the Kneip-Simar (1995) approach.

Suggested Citation

  • SIMAR , Léopold, 1995. "Aspects of Statistical Analysis in DEA-Type Frontier Models," CORE Discussion Papers 1995061, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvco:1995061
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    File URL: https://uclouvain.be/en/research-institutes/immaq/core/dp-1995.html
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    Cited by:

    1. 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.
    2. Evangelia Desli & Subhash C. Ray, 2004. "A Bootstrap-Regression Procedure to Capture Unit Specific Effects In Data Envelopment Analysis," Indian Economic Review, Department of Economics, Delhi School of Economics, vol. 39(1), pages 89-110, January.
    3. Manevska-Tasevska, Gordana & Hansson, Helena, 2010. "Influence of rural development policy targets on farm efficiency: An efficiency study of labour intensive grape growing family farms," IAMO Forum 2010: Institutions in Transition – Challenges for New Modes of Governance 52696, Leibniz Institute of Agricultural Development in Central and Eastern Europe (IAMO).
    4. Kjoeserud,G.G. & Kvamme,O.J. & Kittelsen,S.A.C., 2001. "Errors in survey based quality evaluation variables in efficiency models of primary care physicians," Memorandum 24/2001, Oslo University, Department of Economics.
    5. W. Alexander & Alfred Haug & Mohammad Jaforullah, 2010. "A two-stage double-bootstrap data envelopment analysis of efficiency differences of New Zealand secondary schools," Journal of Productivity Analysis, Springer, vol. 34(2), pages 99-110, October.
    6. Léopold Simar & Paul W. Wilson, 2015. "Statistical Approaches for Non-parametric Frontier Models: A Guided Tour," International Statistical Review, International Statistical Institute, vol. 83(1), pages 77-110, April.
    7. Alois Kneip & Léopold Simar & Paul Wilson, 2011. "A Computationally Efficient, Consistent Bootstrap for Inference with Non-parametric DEA Estimators," Computational Economics, Springer;Society for Computational Economics, vol. 38(4), pages 483-515, November.
    8. Léopold Simar & Paul Wilson, 2011. "Inference by the m out of n bootstrap in nonparametric frontier models," Journal of Productivity Analysis, Springer, vol. 36(1), pages 33-53, August.
    9. Hall, Peter & Park, Byeong U. & Stern, Steven E., 1998. "On Polynomial Estimators of Frontiers and Boundaries," Journal of Multivariate Analysis, Elsevier, vol. 66(1), pages 71-98, July.
    10. Bielecki, Andre & Albers, Sönke, 2012. "Eine Analyse der Forschungseffizienz deutscher betriebswirtschaftlicher Fachbereiche basierend auf den Daten des Centrums für Hochschulentwicklung (CHE)," EconStor Preprints 57429, ZBW - German National Library of Economics.
    11. Dieter Gstach, 1996. "A new approach to stochastic frontier estimation: DEA+," Department of Economics Working Papers wuwp039, Vienna University of Economics and Business, Department of Economics.
    12. Kneip, Alois & Simar, Léopold & Wilson, Paul W., 2008. "Asymptotics And Consistent Bootstraps For Dea Estimators In Nonparametric Frontier Models," Econometric Theory, Cambridge University Press, vol. 24(06), pages 1663-1697, December.
    13. Subodh Kumar & R. Robert Russell, 2002. "Technological Change, Technological Catch-up, and Capital Deepening: Relative Contributions to Growth and Convergence," American Economic Review, American Economic Association, vol. 92(3), pages 527-548, June.
    14. Chambers, Robert G. & Fare, Rolf & Jaenicke, Edward & Lichtenberg, Erik, 1998. "Using dominance in forming bounds on DEA models: The case of experimental agricultural data," Journal of Econometrics, Elsevier, vol. 85(1), pages 189-203, July.
    15. Bielecki, Andre & Albers, Sönke & Mantrala, Murali, 2012. "Salesperson Efficiency Benchmarking Using Sales Response Data: Who is Working Hard and Working Smart?," EconStor Preprints 57427, ZBW - German National Library of Economics.

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