The aim of this paper is to construct a robust nonparametric estimator for the production frontier. We study this problem under a regression model with one-sided errors, where the regression function defines the achievable maximum output, for a given level of inputs-usage, and the regression error defines the inefficiency term. The main tool is a concept of partial regression boundary defined as a special probability-weighted moment. This concept motivates a robustified unconditional alternative to the pioneering class of nonparametric conditional expected maximum production functions. We prove that both the resulting benchmark partial frontier and its estimator share the desirable monotonicity of the true full frontier. We derive the asymptotic properties of the partial and full frontier estimators, and unravel their behavior from a robustness theory point of view. We provide numerical illustrations and Monte Carlo evidence that the presented concept of unconditional expected maximum production functions is more efficient and reliable in filtering out noise than the original conditional version. The methodology is very easy and fast to implement. Its usefulness is discussed through two concrete datasets from the sector of Delivery Services, where outliers are likely to affect the traditional conditional approach.

中文翻译：

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强化预期的最大生产边界

本文的目的是为生产边界构建一个稳健的非参数估计器。我们在具有单边误差的回归模型下研究这个问题，其中回归函数定义了给定输入使用水平的可实现的最大输出，回归误差定义了低效率项。主要工具是定义为特殊概率加权矩的部分回归边界的概念。这个概念激发了一种鲁棒的无条件替代方案，以替代开创性的非参数条件预期最大生产函数。我们证明了得到的基准部分边界及其估计器都具有真正完整边界的理想单调性。我们推导出部分和完全前沿估计量的渐近性质，并从稳健性理论的角度解开他们的行为。我们提供了数值插图和蒙特卡罗证据，证明所提出的无条件预期最大生产函数概念在滤除噪声方面比原始条件版本更有效和可靠。该方法非常容易和快速实施。它的有用性通过交付服务部门的两个具体数据集进行了讨论，其中异常值可能会影响传统的条件方法。