Robust frontier estimation from noisy data: A Tikhonov regularization approach

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 ill-posed 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.

Measuring the Cost Efficiency of Lebanese Commercial Banks using the Stochastic Frontier Approach

“…The justification for such a breakdown comes down to the idea that a production process whose planning has been prepared in an optimal way ex-ante can provide partly random production levels. This is how it is possible for some units, through the use of the stochastic frontier, to lie above the frontier (Daouia et al 2020). This situation occurs when a unit has not only ensured an optimal planning of its production process but has also taken advantage of more beneficial states of effects or random variables than the average.…”

Nonparametric, Stochastic Frontier Models with Multiple Inputs and Outputs

“…Here again the numerical burden is significant. Daouia et al (2020) use an alternative approach based on nonparametric estimation of the conditional survival function of U | Z, but for identification must assume that the noise follows a fully known distribution, e.g., | z ∼ N (0, σ 2 (z)) where σ 2 (z) is known.…”

Estimation of the Boundary of a Variable Observed With Symmetric Error

“…Goldenshluger and Tsybakov (2004), Delaigle and Gijbels (2006), Meister (2006a), and Aarts, Groeneboom and Jongbloed (2007), among others. The assumption that the distribution of ε is given, is a strong hypothesis (see Daouia et al, 2018). However, it has been shown that thanks to the positivity of Z the variance of ε is identified if ε is normally distributed (see Schwarz and Van Bellegem, 2010), and in that case the minimum τ may be estimated nonparametrically (see Kneip et al, 2015).…”