Regularization of Nonparametric Frontier Estimators
In production theory and efficiency analysis, we are interested in estimating the production frontier which is the locus of the maximal attainable level of an output (the production), given a set of inputs (the production factors). In other setups, we are rather willing to estimate an input (or cost) frontier that is defined as 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. The basic tool is the order-m partial frontier where we let the order m to converge to infinity when n ! 1 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 estimator which, in addition, is more robust to extreme values and outliers than the usual nonparametric frontier estimators, like FDH. The performances of our estimators are evaluated in finite samples through some Monte-Carlo experiments. We illustrate also how to provide, in an easy way, confidence intervals for the frontier function both with a simulated data set and a real data set.
|Date of creation:||Sep 2009|
|Date of revision:|
|Publication status:||Published in Journal of Econometrics, vol.�168, n°2, juin 2012, p.�285-299.|
|Contact details of provider:|| Postal: |
Phone: +33 (0)5 61 12 85 89
Fax: + 33 (0)5 61 12 86 37
Web page: http://www.idei.fr/
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Abdelaati Daouia & Irène Gijbels, 2011. "Robustness and inference in nonparametric partial-frontier modeling," Post-Print peer-00796744, HAL.
- 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.
- 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.
- Daouia, Abdelaati & Simar, Léopold, 2005. "Robust nonparametric estimators of monotone boundaries," Journal of Multivariate Analysis, Elsevier, vol. 96(2), pages 311-331, October.
- Kneip, Alois & Simar, Léopold & Wilson, Paul W., 2008.
"Asymptotics And Consistent Bootstraps For Dea Estimators In Nonparametric Frontier Models,"
Cambridge University Press, vol. 24(06), pages 1663-1697, December.
- Alois Kneip & Léopold Simar & Paul W. Wilson, 2006. "Asymptotics and Consistent Bootstraps for DEA Estimators in Non-parametric Frontier Models," Bonn Econ Discussion Papers bgse12_2006, University of Bonn, Germany.
- Daouia, Abdelaati & Simar, Leopold, 2007. "Nonparametric efficiency analysis: A multivariate conditional quantile approach," Journal of Econometrics, Elsevier, vol. 140(2), pages 375-400, October.
When requesting a correction, please mention this item's handle: RePEc:ide:wpaper:22808. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ()
If references are entirely missing, you can add them using this form.