IDEAS home Printed from https://ideas.repec.org/p/tse/wpaper/22818.html
   My bibliography  Save this paper

Frontier Estimation and Extreme Values Theory

Author

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

Abstract

In this paper we investigate the problem of nonparametric monotone frontier estimation from an extreme-values theory perspective. This allows to revisit the asymptotic theory of the popular Free Disposal Hull estimator in a general setup, to derive new and asymptotically Gaussian estimators and to provide useful asymptotic confidence bands for the monotone boundary function. The finite sample behavior of the suggested estimators is explored through Monte-Carlo experiments. We also apply our approach to a real data set on the production activity of the French postal services.

Suggested Citation

  • Daouia, Abdelaati & Florens, Jean-Pierre & Simar, Léopold, 2009. "Frontier Estimation and Extreme Values Theory," TSE Working Papers 10-165, Toulouse School of Economics (TSE).
    • Handle: RePEc:tse:wpaper:22818
    as

    Download full text from publisher

    File URL: http://www.tse-fr.eu/sites/default/files/medias/doc/wp/etrie/10-165.pdf
    File Function: Full text
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Tsybakov, A.B. & Korostelev, A.P. & Simar, L., 1992. "Efficient Estimation of Monotone Boundaries," Papers 9209, Catholique de Louvain - Institut de statistique.
    2. 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.
    3. 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.
    4. 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.
    5. Hwang, J. H. & Park, B. U. & Ryu, W., 2002. "Limit theorems for boundary function estimators," Statistics & Probability Letters, Elsevier, vol. 59(4), pages 353-360, October.
    6. 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.
    7. Aragon, Y. & Daouia, A. & Thomas-Agnan, C., 2005. "Nonparametric Frontier Estimation: A Conditional Quantile-Based Approach," Econometric Theory, Cambridge University Press, vol. 21(2), pages 358-389, April.
    8. Korostelev, A. P. & Simar, L. & Tsybakov, A. B., 1995. "Estimation of monotone boundaries," LIDAM Reprints CORE 1178, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    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. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Abdelaati Daouia & Léopold Simar & Paul W. Wilson, 2017. "Measuring firm performance using nonparametric quantile-type distances," Econometric Reviews, Taylor & Francis Journals, vol. 36(1-3), pages 156-181, March.
    2. Simar, Léopold & Vanhems, Anne, 2012. "Probabilistic characterization of directional distances and their robust versions," Journal of Econometrics, Elsevier, vol. 166(2), pages 342-354.
    3. Daouia, Abdelaati & Florens, Jean-Pierre & Simar, Léopold, 2012. "Regularization of nonparametric frontier estimators," Journal of Econometrics, Elsevier, vol. 168(2), pages 285-299.
    4. Abdelaati Daouia & Hohsuk Noh & Byeong U. Park, 2016. "Data envelope fitting with constrained polynomial splines," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(1), pages 3-30, January.
    5. Abdelaati Daouia & Irène Gijbels, 2011. "Robustness and inference in nonparametric partial-frontier modeling," Post-Print hal-00796744, HAL.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Girard, Stéphane & Jacob, Pierre, 2008. "Frontier estimation via kernel regression on high power-transformed data," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 403-420, March.
    2. Abdelaati Daouia & Hohsuk Noh & Byeong U. Park, 2016. "Data envelope fitting with constrained polynomial splines," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(1), pages 3-30, January.
    3. 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).
    4. 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.
    5. Girard, Séphane & Jacob, Pierre, 2009. "Frontier estimation with local polynomials and high power-transformed data," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1691-1705, September.
    6. 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.
    7. Cheng, Ming-Yen & Hall, Peter, 2006. "Methods for tracking support boundaries with corners," Journal of Multivariate Analysis, Elsevier, vol. 97(8), pages 1870-1893, September.
    8. 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.
    9. Wheelock, David C. & Wilson, Paul W., 2008. "Non-parametric, unconditional quantile estimation for efficiency analysis with an application to Federal Reserve check processing operations," Journal of Econometrics, Elsevier, vol. 145(1-2), pages 209-225, July.
    10. Florens, Jean-Pierre & Simar, Leopold, 2005. "Parametric approximations of nonparametric frontiers," Journal of Econometrics, Elsevier, vol. 124(1), pages 91-116, January.
    11. Martins-Filho, Carlos & Yao, Feng, 2007. "Nonparametric frontier estimation via local linear regression," Journal of Econometrics, Elsevier, vol. 141(1), pages 283-319, November.
    12. Hall, Peter & Park, Byeong U., 2004. "Bandwidth choice for local polynomial estimation of smooth boundaries," Journal of Multivariate Analysis, Elsevier, vol. 91(2), pages 240-261, November.
    13. Abdelaati Daouia & Léopold Simar & Paul W. Wilson, 2017. "Measuring firm performance using nonparametric quantile-type distances," Econometric Reviews, Taylor & Francis Journals, vol. 36(1-3), pages 156-181, March.
    14. 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.
    15. Martins-Filho, Carlos & Yao, Feng, 2008. "A smooth nonparametric conditional quantile frontier estimator," Journal of Econometrics, Elsevier, vol. 143(2), pages 317-333, April.
    16. U. Park, Byeong, 2001. "On estimating the slope of increasing boundaries," Statistics & Probability Letters, Elsevier, vol. 52(1), pages 69-72, March.
    17. Klemelä, Jussi, 2004. "Complexity penalized support estimation," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 274-297, February.
    18. Carlos Martins-FIlho & Feng Yao, 2004. "A Nonparametric Model of Frontiers," Econometric Society 2004 Latin American Meetings 102, Econometric Society.
    19. Simar, Léopold & Vanhems, Anne, 2012. "Probabilistic characterization of directional distances and their robust versions," Journal of Econometrics, Elsevier, vol. 166(2), pages 342-354.
    20. Amparo Soler Domínguez & Juan Carlos Matallín Sáez & Emili Tortosa Ausina, 2011. "On the informativeness of persistence for mutual funds' performance evaluation using partial frontiers," Working Papers. Serie EC 2011-08, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:tse:wpaper:22818. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/tsetofr.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.