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B0627
Title: Nonparametric robust stochastic frontier analysis: A Tikhonov regularization approach Authors:  Jean-Pierre Florens - Toulouse School of Economics (France) [presenting]
Abdelaati Daouia - Toulouse School of Economics (France)
Leopold Simar - Universite Catholique de Louvain (Belgium)
Abstract: In production theory and efficiency analysis, the interest is in estimating frontiers of the production set, i.e. the set of attainable combinations of inputs (the resources or production factors) and of outputs (the production: goods or services produced. We suggest an original and new approach to estimate non-parametrically and in a robust way stochastic frontier functions, i.e. frontier models where stochastic noise is allowed. We suppose that the noise has a given density (like the Gaussian) for identifiability. We suppose, as in most studies on deconvolution, that the variance of the noise is known. We consider the estimation of an minimum input (or cost) function reachable for given values of the outputs. The idea is to use deconvolution methods to estimate in a first step and for each value of the outputs, the conditional survivor function, as in previous deterministic models where no noise was allowed. This provides an estimate of the order-$m$ frontier by integrating powers of the estimated survivor function. The asymptotic of the resulting estimators is derived and under some regularity condition, we reach the $\sqrt{n}$ rate of convergence and asymptotic normality. The procedure is based on Tikhonov regularization which is easy and fast to implement. It is illustrated with simulated and real data examples.