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Regularization of nonparametric frontier estimators

Author

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  • Daouia, Abdelaati
  • Florens, Jean-Pierre
  • Simar, Léopold

Abstract

In production theory and efficiency analysis, we estimate the production frontier, the locus of the maximal attainable level of an output (the production), given a set of inputs (the production factors). In other setups, we estimate rather an input (or cost) frontier, the minimal level of the input (cost) attainable for a given set of outputs (goods or services produced). In both cases the problem can be viewed as estimating a surface under shape constraints (monotonicity, …). In this paper we derive the theory of an estimator of the frontier having an asymptotic normal distribution. It is based on the order-m partial frontier where we let the order m to converge to infinity when n→∞ but at a slow rate. The final estimator is then corrected for its inherent bias. We thus can view our estimator as a regularized frontier. In addition, the estimator is more robust to extreme values and outliers than the usual nonparametric frontier estimators, like FDH and than the unregularized order-mn estimator of Cazals et al. (2002) converging to the frontier with a Weibull distribution if mn→∞ fast enough when n→∞. The performances of our estimators are evaluated in finite samples and compared to other estimators through some Monte-Carlo experiments, showing a better behavior (in terms of robustness, bias, MSE and achieved coverage of the resulting confidence intervals). The practical implementation and the robustness properties are illustrated through simulated data sets but also with a real data set.

Suggested Citation

  • Daouia, Abdelaati & Florens, Jean-Pierre & Simar, Léopold, 2012. "Regularization of nonparametric frontier estimators," Journal of Econometrics, Elsevier, vol. 168(2), pages 285-299.
  • Handle: RePEc:eee:econom:v:168:y:2012:i:2:p:285-299
    DOI: 10.1016/j.jeconom.2012.01.032
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    References listed on IDEAS

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    1. Daouia, Abdelaati & Simar, Léopold, 2005. "Robust nonparametric estimators of monotone boundaries," Journal of Multivariate Analysis, Elsevier, vol. 96(2), pages 311-331, October.
    2. 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.
    3. Daouia, Abdelaati & Florens, Jean-Pierre & Simar, Léopold, 2009. "Frontier Estimation and Extreme Values Theory," TSE Working Papers 10-165, Toulouse School of Economics (TSE).
    4. 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.
    5. 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.
    6. repec:hal:journl:peer-00796744 is not listed on IDEAS
    7. Daouia, Abdelaati & Gijbels, Irène, 2011. "Robustness and inference in nonparametric partial frontier modeling," Journal of Econometrics, Elsevier, vol. 161(2), pages 147-165, April.
    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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    Citations

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    Cited by:

    1. Florens, Jean-Pierre & Schwarz, Maik & Van Bellegem, Sébastien, 2010. "Nonparametric Frontier Estimation from Noisy Data," TSE Working Papers 10-179, Toulouse School of Economics (TSE).
    2. Florens, Jean-Pierre & Simoni, Anna, 2016. "Regularizing Priors For Linear Inverse Problems," Econometric Theory, Cambridge University Press, vol. 32(01), pages 71-121, February.
    3. Girard, Stéphane & Guillou, Armelle & Stupfler, Gilles, 2013. "Frontier estimation with kernel regression on high order moments," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 172-189.
    4. Song, Junmo & Oh, Dong-hyun & Kang, Jiwon, 2017. "Robust estimation in stochastic frontier models," Computational Statistics & Data Analysis, Elsevier, vol. 105(C), pages 243-267.
    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. repec:sbe:breart:v:33:y:2013:i:2:a:26508 is not listed on IDEAS
    7. Daouia, Abdelaati & Florens, Jean-Pierre & Simar, Léopold, 2018. "Robustified expected maximum production frontiers," TSE Working Papers 17-890, Toulouse School of Economics (TSE).
    8. 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.
    9. Simar, Léopold & Vanhems, Anne, 2012. "Probabilistic characterization of directional distances and their robust versions," Journal of Econometrics, Elsevier, vol. 166(2), pages 342-354.
    10. Daouia, Abdelaati & Florens, Jean-Pierre & Simar, Léopold, 2016. "Robust frontier estimation from noisy data: a Tikhonov regularization approach," TSE Working Papers 16-665, Toulouse School of Economics (TSE), revised Feb 2018.
    11. Cazals, Catherine & Fève, Frédérique & Florens, Jean-Pierre & Simar, Léopold, 2016. "Nonparametric instrumental variables estimation for efficiency frontier," Journal of Econometrics, Elsevier, vol. 190(2), pages 349-359.
    12. repec:kap:jculte:v:41:y:2017:i:2:d:10.1007_s10824-017-9295-z is not listed on IDEAS
    13. 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).

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