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A Γ-moment approach to monotonic boundary estimation

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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. 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.
    2. Daouia, Abdelaati & Simar, Léopold, 2005. "Robust nonparametric estimators of monotone boundaries," Journal of Multivariate Analysis, Elsevier, vol. 96(2), pages 311-331, October.
    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(6), pages 1663-1697, December.
    4. 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.
    5. 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.
    6. 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.
    7. Park, B.U. & Simar, L. & Weiner, Ch., 2000. "The Fdh Estimator For Productivity Efficiency Scores," Econometric Theory, Cambridge University Press, vol. 16(6), pages 855-877, December.
    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. Dominique Deprins & Léopold Simar & Henry Tulkens, 2006. "Measuring Labor-Efficiency in Post Offices," Springer Books, in: Parkash Chander & Jacques Drèze & C. Knox Lovell & Jack Mintz (ed.), Public goods, environmental externalities and fiscal competition, chapter 0, pages 285-309, Springer.
    10. Stéphane Girard & Armelle Guillou & Gilles Stupfler, 2012. "Estimating an endpoint with high-order moments," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(4), pages 697-729, December.
    11. 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.
    12. 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.
    13. 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, March.
    14. Park, B.U. & Jeong, S.-O. & Simar, L., 2010. "Asymptotic distribution of conical-hull estimators of directional edges," LIDAM Reprints ISBA 2010025, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
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    Cited by:

    1. Daouia, Abdelaati & Florens, Jean-Pierre & Simar, Léopold, 2020. "Robust frontier estimation from noisy data: A Tikhonov regularization approach," Econometrics and Statistics, Elsevier, vol. 14(C), pages 1-23.
    2. Daouia, Abdelaati & Laurent, Thibault & Noh, Hohsuk, 2017. "npbr: A Package for Nonparametric Boundary Regression in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 79(i09).
    3. Daouia, Abdelaati & Florens, Jean-Pierre & Simar, Léopold, 2021. "Robustified Expected Maximum Production Frontiers," Econometric Theory, Cambridge University Press, vol. 37(2), pages 346-387, April.

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    More about this item

    Keywords

    Cost function; Edge data; Extreme-value index; Free disposal hull; Moment frontier;
    All these keywords.

    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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