Estimating Frontier Cost Models Using Extremiles



In the econometric literature on the estimation of production technologies, there has been considerable interest in estimating so called cost frontier models that relate closely to models for extreme non-standard conditional quantiles (Aragon et al. Econ Theor 21:358–389, 2005) and expected minimum input functions (Cazals et al. J Econometrics 106:1–25, 2002). In this paper, we introduce a class of extremile-based cost frontiers which includes the family of expected minimum input frontiers and parallels the class of quantile-type frontiers. The class is motivated via several angles, which reveals its specific merits and strengths. We discuss nonparametric estimation of the extremile-based costs frontiers and establish asymptotic normality and weak convergence of the associated process. Empirical illustrations are provided.


Cost Function Joint Density Tail Index Stochastic Frontier Model Free Disposal Hull 
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This research was supported by the French “Agence Nationale pour la Recherche” under grant ANR-08-BLAN-0106-01/EPI project (Abdelaati Daouia) and the Research Fund KULeuven (GOA/07/04-project) and by the IAP research network P6/03, Federal Science Policy, Belgium (Irène Gijbels).


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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Toulouse School of Economics (GREMAQ)University of ToulouseToulouseFrance
  2. 2.Department of Mathematics and Leuven Statistics Research CenterKatholieke Universiteit LeuvenLeuven (Heverlee)Belgium

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