Benchmarking tools, including stochastic frontier analysis (SFA), data envelopment analysis (DEA), and its stochastic extension (StoNED) are core tools in economics used to estimate an efficiency envelope and production inefficiencies from data. The problem appears in a wide range of fields -- for example, in global health the frontier can quantify efficiency of interventions and funding of health initiatives. Despite their wide use, classic benchmarking approaches have key limitations that preclude even wider applicability. Here we propose a robust non-parametric stochastic frontier meta-analysis (SFMA) approach that fills these gaps. First, we use flexible basis splines and shape constraints to model the frontier function, so specifying a functional form of the frontier as in classic SFA is no longer necessary. Second, the user can specify relative errors on input datapoints, enabling population-level analyses. Third, we develop a likelihood-based trimming strategy to robustify the approach to outliers, which otherwise break available benchmarking methods. We provide a custom optimization algorithm for fast and reliable performance. We implement the approach and algorithm in an open source Python package `sfma'. Synthetic and real examples show the new capabilities of the method, and are used to compare SFMA to state of the art benchmarking packages that implement DEA, SFA, and StoNED.

翻译：基准测试工具，包括随机前沿分析（SFA）、数据包络分析（DEA）及其随机扩展方法（StoNED），是经济学中用于根据数据估计效率边界与生产无效率的核心工具。该问题广泛应用于多个领域——例如，在全球健康领域，效率边界可量化干预措施与健康项目资金的使用效率。尽管应用广泛，经典基准测试方法存在关键局限性，阻碍了其更广范围的适用性。本文提出一种鲁棒的非参数随机前沿元分析（SFMA）方法，以填补这些空白。首先，我们采用灵活基样条与形状约束对前沿函数进行建模，从而无需像经典SFA那样指定前沿的函数形式。其次，用户可指定输入数据点的相对误差，使群体层面分析成为可能。第三，我们开发了基于似然的修剪策略，以增强方法对异常值的鲁棒性——而异常值通常会破坏现有基准测试方法的有效性。我们提供定制化优化算法以实现快速可靠的性能，并将该方法和算法在开源Python包`sfma`中实现。合成数据与真实案例展示了该方法的新能力，并用于将SFMA与实现DEA、SFA和StoNED的顶尖基准测试软件包进行对比。