Regularization of Nonparametric Frontier Estimators
AbstractIn 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.
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Bibliographic InfoPaper provided by Institut d'Économie Industrielle (IDEI), Toulouse in its series IDEI Working Papers with number 614.
Date of creation: Sep 2009
Date of revision:
Publication status: Published in Journal of Econometrics, vol.�168, n°2, juin 2012, p.�285-299.
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Other versions of this item:
- Daouia, Abdelaati & Florens, Jean-Pierre & Simar, Léopold, 2012. "Regularization of nonparametric frontier estimators," Journal of Econometrics, Elsevier, vol. 168(2), pages 285-299.
- Daouia, Abdelaati & Florens, Jean-Pierre & Simar, Léopold, 2009. "Regularization of Nonparametric Frontier Estimators," TSE Working Papers 10-168, Toulouse School of Economics (TSE).
- NEP-ALL-2010-07-31 (All new papers)
- NEP-ECM-2010-07-31 (Econometrics)
- NEP-EFF-2010-07-31 (Efficiency & Productivity)
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- 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.
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- 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.
- Jean-Pierre Florens & Anna Simoni, 2013. "Regularizing Priors for Linear Inverse Problems," Working Papers hal-00873180, HAL.
- Anna Simoni & Jean-Pierre Florens, 2013. "Regularizing Priors for Linear Inverse Problems," THEMA Working Papers 2013-32, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
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