Nonparametric conditional efficiency measures: asymptotic properties

Cazals et al. (J. Econom. 106: 1–25, 2002 ), Daraio and Simar (J. Prod. Anal. 24: 93–121, 2005 ; Advanced Robust and Nonparametric Methods in Efficiency Analysis, 2007a ; J. Prod. Anal. 28: 13–32, 2007b ) developed a conditional frontier model which incorporates the environmental factors into measuring the efficiency of a production process in a fully nonparametric setup. They also provided the corresponding nonparametric efficiency measures: conditional FDH estimator, conditional DEA estimator. The two estimators have been applied in the literature without any theoretical background about their statistical properties. The aim of this paper is to provide an asymptotic analysis (i.e. asymptotic consistency and limit sampling distribution) of the conditional FDH and conditional DEA estimators.