Single Index Models for nonparametric conditional frontiers

Catherine Cazals, Jean-Pierre Florens and Léopold Simar
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Catherine Cazals: Toulouse School of Economics
Jean-Pierre Florens: Toulouse School of Economics
Léopold Simar: Université catholique de Louvain, LIDAM/ISBA, Belgium

No 2026015, LIDAM Reprints ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

Abstract: In production theory, attention has been paid to the analysis of the impact of environmental variables on the efficiency of firms. The standard approach to this problem is to use conditional frontier models. For nonparametric approaches, this may create serious problems if the number of environmental factors increases, exacerbating the curse of dimensionality inherent in such models. In order to address this issue, it is investigated whether Single Index Models (SIM) could be used for modeling the effect of these variables on the production process. A test is proposed for the SIM hypothesis and the asymptotic properties are analyzed. If the SIM model is not rejected, better rates of convergence of the conditional efficiency estimates are obtained. The finite sample properties of the proposed test and the properties of the resulting estimates of the SIM, when it is not rejected, are investigated through Monte Carlo experiments. The method is illustrated with a real data set from the French national postal operator in charge of universal service.

Keywords: Nonparametric conditional frontier; Single-Index; Robust frontier; Environmental variables (search for similar items in EconPapers)
JEL-codes: C10 C14 C51 D22 (search for similar items in EconPapers)
Pages: 30
Date: 2026-04-18
Note: In: Econometrics and Statistics, 2026
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Persistent link: https://EconPapers.repec.org/RePEc:aiz:louvar:2026015

DOI: 10.1016/j.ecosta.2026.04.001

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