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A Γ-moment approach to monotonic boundary estimation

Author

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  • Daouia, Abdelaati
  • Girard, Stéphane
  • Guillou, Armelle

Abstract

The estimation of optimal support boundaries under the monotonicity constraint is relatively unexplored and still in full development. This article examines a new extreme-value based model which provides a valid alternative for complete envelopment frontier models that often suffer from lack of precision, and for purely stochastic ones that are known to be sensitive to model misspecification. We provide different motivating applications including the estimation of the minimal cost in production activity and the assessment of the reliability of nuclear reactors.

Suggested Citation

  • Daouia, Abdelaati & Girard, Stéphane & Guillou, Armelle, 2014. "A Γ-moment approach to monotonic boundary estimation," Journal of Econometrics, Elsevier, vol. 178(2), pages 727-740.
  • Handle: RePEc:eee:econom:v:178:y:2014:i:2:p:727-740
    DOI: 10.1016/j.jeconom.2013.10.013
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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. Hall, Peter & Nussbaum, Michael & Stern, Steven E., 1997. "On the Estimation of a Support Curve of Indeterminate Sharpness," Journal of Multivariate Analysis, Elsevier, vol. 62(2), pages 204-232, August.
    3. 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.
    4. Abdelaati Daouia & Byeong U. Park, 2013. "On Projection-type Estimators of Multivariate Isotonic Functions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(2), pages 363-386, June.
    5. 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.
    6. Einmahl, J. H.J. & Dekkers, A. L.M. & de Haan, L., 1989. "A moment estimator for the index of an extreme-value distribution," Other publications TiSEM 81970cb3-5b7a-4cad-9bf6-2, Tilburg University, School of Economics and Management.
    7. Girard, Stéphane & Guillou, Armelle & Stupfler, Gilles, 2012. "Estimating an endpoint with high order moments in the Weibull domain of attraction," Statistics & Probability Letters, Elsevier, vol. 82(12), pages 2136-2144.
    8. 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.
    9. Hardle, W. & Park, B. U. & Tsybakov, A. B., 1995. "Estimation of Non-sharp Support Boundaries," Journal of Multivariate Analysis, Elsevier, vol. 55(2), pages 205-218, November.
    10. S.-O. Jeong & B. U. Park, 2006. "Large Sample Approximation of the Distribution for Convex-Hull Estimators of Boundaries," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(1), pages 139-151.
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    Citations

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    Cited by:

    1. Daouia, Abdelaati & Florens, Jean-Pierre & Simar, Léopold, 2018. "Robustified expected maximum production frontiers," TSE Working Papers 17-890, Toulouse School of Economics (TSE).
    2. 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.
    3. 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).

    More about this item

    Keywords

    Cost function; Edge data; Extreme-value index; Free disposal hull; Moment frontier;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • D20 - Microeconomics - - Production and Organizations - - - General

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