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NONPARAMETRIC FRONTIER ESTIMATION: A CONDITIONAL QUANTILE-BASED APPROACH

Published online by Cambridge University Press:  31 March 2005

Y. Aragon ,
A. Daouia  and
C. Thomas-Agnan
Y. Aragon
Affiliation:
Groupe de Recherche en Economie Mathématique et Quantitative et Laboratoire de Statistique et Probabilités, Université de Toulouse
A. Daouia
Affiliation:
Groupe de Recherche en Economie Mathématique et Quantitative et Laboratoire de Statistique et Probabilités, Université de Toulouse
C. Thomas-Agnan
Affiliation:
Groupe de Recherche en Economie Mathématique et Quantitative et Laboratoire de Statistique et Probabilités, Université de Toulouse
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Abstract

In frontier analysis, most of the nonparametric approaches (free disposal hull [FDH], data envelopment analysis [DEA]) are based on envelopment ideas, and their statistical theory is now mostly available. However, by construction, they are very sensitive to outliers. Recently, a robust nonparametric estimator has been suggested by Cazals, Florens, and Simar (2002, Journal of Econometrics 1, 1–25). In place of estimating the full frontier, they propose rather to estimate an expected frontier of order m. Similarly, we construct a new nonparametric estimator of the efficient frontier. It is based on conditional quantiles of an appropriate distribution associated with the production process. We show how these quantiles are interesting in efficiency analysis. We provide the statistical theory of the obtained estimators. We illustrate with some simulated examples and a frontier analysis of French post offices, showing the advantage of our estimators compared with the estimators of the expected maximal output frontiers of order m.We thank J.P. Florens for helpful discussions and C. Cazals for providing the post office data set. We also are very grateful to the referees for useful suggestions.

Type
Research Article
Information
Econometric Theory , Volume 21 , Issue 2 , April 2005 , pp. 358 - 389
Copyright
© 2005 Cambridge University Press

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