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Résumé de communication

Résumé 273 :

Boundary estimation in the presence of measurement error with unknown variance
Van Keilegom, Ingrid ; Kneip, Alois ; Simar, Léopold
Université catholique de Louvain

Boundary estimation appears naturally in economics in the context of productivity analysis. The performance of a firm is measured by the distance between its achieved output level (quantity of goods produced) and an optimal production frontier which is the locus of the maximal achievable output given the level of the inputs (labor, energy, capital, etc.). Frontier estimation becomes difficult if the outputs are measured with noise and most approaches rely on restrictive parametric assumptions. This paper contributes to the direction of nonparametric approaches. We consider a general setup with unknown frontier and unknown variance of a normally distributed error term, and we propose a nonparametric method which allows to identify and estimate both quantities simultaneously. The asymptotic consistency and the rate of convergence of our estimators are established, and simulations are carried out to verify the performance of the estimators for small samples. We also apply our method on a dataset concerning the production output of American electricity utility companies.