Robust frontier estimation from noisy data: a Tikhonov regularization approach

Abdelaati Daouia (), Jean-Pierre Florens () and Leopold Simar
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Abdelaati Daouia: TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement
Jean-Pierre Florens: TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement

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Abstract: In stochastic frontier models, the regression function defines the production frontier and the regression errors are assumed to be composite. The actually observed outputs are assumed to be contaminated by a stochastic noise. The additive regression errors are composed from this noise term and the one-sided inefficiency term. The aim is to construct a robust nonparametric estimator for the production function. The main tool is a robust concept of partial, expected maximum production frontier, defined as a special probability-weighted moment. In contrast to the deterministic one-sided error model where robust partial frontier modeling is fruitful, the composite error problem requires a substantial different treatment based on deconvolution techniques. To ensure the identifiability of the model, it is sufficient to assume an independent Gaussian noise. In doing so, the frontier estimation necessitates the computation of a survival function estimator from an illposed equation. A Tikhonov regularized solution is constructed and nonparametric frontier estimation is performed. The asymptotic properties of the obtained survival function and frontier estimators are established. Practical guidelines to effect the necessary computations are described via a simulated example. The usefulness of the approach is discussed through two concrete data sets from the sector of Delivery Services.

Keywords: Deconvolution; Nonparametric estimation; Probability-weighted moment; Production function; Robustness; Stochastic frontie; Tikhonov regularization (search for similar items in EconPapers)
Date: 2020-04-27
New Economics Papers: this item is included in nep-eff and nep-ore
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Published in Econometrics and Statistics , 2020, 14, pp.1-23. ⟨10.1016/j.ecosta.2018.07.003⟩

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Related works:
Journal Article: Robust frontier estimation from noisy data: A Tikhonov regularization approach (2020)
Working Paper: Robust frontier estimation from noisy data: a Tikhonov regularization approach (2018)
Working Paper: Robust frontier estimation from noisy data: a Tikhonov regularization approach (2016)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-02573853

DOI: 10.1016/j.ecosta.2018.07.003

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