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Robustness and inference in nonparametric partial frontier modeling

Author

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  • Daouia, Abdelaati
  • Gijbels, Irène

Abstract

A major aim in recent nonparametric frontier modeling is to estimate a partial frontier well inside the sample of production units but near the optimal boundary. Two concepts of partial boundaries of the production set have been proposed: an expected maximum output frontier of order m=1,2,... and a conditional quantile-type frontier of order [alpha][set membership, variant]]0,1]. In this paper, we answer the important question of how the two families are linked. For each m, we specify the order [alpha] for which both partial production frontiers can be compared. We show that even one perturbation in data is sufficient for breakdown of the nonparametric order-m frontiers, whereas the global robustness of the order-[alpha] frontiers attains a higher breakdown value. Nevertheless, once the [alpha] frontiers break down, they become less resistant to outliers than the order-m frontiers. Moreover, the m frontiers have the advantage to be statistically more efficient. Based on these findings, we suggest a methodology for identifying outlying data points. We establish some asymptotic results, contributing to important gaps in the literature. The theoretical findings are illustrated via simulations and real data.

Suggested Citation

  • Daouia, Abdelaati & Gijbels, Irène, 2011. "Robustness and inference in nonparametric partial frontier modeling," Journal of Econometrics, Elsevier, vol. 161(2), pages 147-165, April.
  • Handle: RePEc:eee:econom:v:161:y:2011:i:2:p:147-165
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    References listed on IDEAS

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    1. Aragon, Y. & Daouia, A. & Thomas-Agnan, C., 2005. "Nonparametric Frontier Estimation: A Conditional Quantile-Based Approach," Econometric Theory, Cambridge University Press, vol. 21(02), pages 358-389, April.
    2. Wilson, Paul W, 1993. "Detecting Outliers in Deterministic Nonparametric Frontier Models with Multiple Outputs," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(3), pages 319-323, July.
    3. GIJBELS, Irène & MAMMEN, Enno & PARK, Byeong U. & SIMAR, Léopold, 1997. "On estimation of monotone and concave frontier functions," CORE Discussion Papers 1997031, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    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, vol. 27(6), pages 668-697, June.
    5. Léopold Simar, 2003. "Detecting Outliers in Frontier Models: A Simple Approach," Journal of Productivity Analysis, Springer, vol. 20(3), pages 391-424, November.
    6. Florens, Jean-Pierre & Simar, Leopold, 2005. "Parametric approximations of nonparametric frontiers," Journal of Econometrics, Elsevier, vol. 124(1), pages 91-116, January.
    7. 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.
    8. Daouia, Abdelaati & Simar, Leopold, 2007. "Nonparametric efficiency analysis: A multivariate conditional quantile approach," Journal of Econometrics, Elsevier, vol. 140(2), pages 375-400, October.
    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.
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    Cited by:

    1. Pérez-López, Gemma & Prior, Diego & Zafra-Gómez, José Luis & Plata-Díaz, Ana María, 2016. "Cost efficiency in municipal solid waste service delivery. Alternative management forms in relation to local population size," European Journal of Operational Research, Elsevier, vol. 255(2), pages 583-592.
    2. Christopher Bruffaerts & Bram De Rock & Catherine Dehon, 2014. "Outlier Detection in Nonparametric Frontier Models," Working Papers ECARES ECARES 2014-12, ULB -- Universite Libre de Bruxelles.
    3. Bruffaerts, C. & De Rock, B. & Dehon, C., 2013. "The robustness of the hyperbolic efficiency estimator," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 349-363.
    4. repec:kap:jproda:v:48:y:2017:i:1:d:10.1007_s11123-017-0500-z is not listed on IDEAS
    5. Xia, X.H. & Chen, Y.B. & Li, J.S. & Tasawar, H. & Alsaedi, A. & Chen, G.Q., 2014. "Energy regulation in China: Objective selection, potential assessment and responsibility sharing by partial frontier analysis," Energy Policy, Elsevier, vol. 66(C), pages 292-302.
    6. K Hervé Dakpo, 2016. "On modeling pollution-generating technologies: a new formulation of the by-production approach," Working Papers SMART - LERECO 16-06, INRA UMR SMART-LERECO.
    7. Krüger, Jens J., 2012. "A Monte Carlo study of old and new frontier methods for efficiency measurement," European Journal of Operational Research, Elsevier, pages 137-148.
    8. Daouia, Abdelaati & Florens, Jean-Pierre & Simar, Léopold, 2012. "Regularization of nonparametric frontier estimators," Journal of Econometrics, Elsevier, pages 285-299.
    9. Christopher Bruffaerts & Bram De Rock & Catherine Dehon, 2013. "The Research Efficiency of US Universities: a Nonparametric Frontier Modelling Approach," Working Papers ECARES ECARES 2013-31, ULB -- Universite Libre de Bruxelles.
    10. Meryem Duygun & Huseyin Ozturk & Mohamed Shaban & Emili Tortosa-Ausina, 2014. "Quo Vadis, raters? A frontier approach to identify misratings in sovereign credit risk," Working Papers 2014/10, Economics Department, Universitat Jaume I, Castellón (Spain).
    11. Daouia, Abdelaati & Laurent, Thibault & Noh, Hohsuk, 2015. "npbr: A Package for Nonparametric Boundary Regression in R," TSE Working Papers 15-576, Toulouse School of Economics (TSE).
    12. Abdelsalam, Omneya & Duygun, Meryem & Matallín-Sáez, Juan Carlos & Tortosa-Ausina, Emili, 2014. "Do ethics imply persistence? The case of Islamic and socially responsible funds," Journal of Banking & Finance, Elsevier, vol. 40(C), pages 182-194.

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