Daouia, AbdelaatiORCID: https://orcid.org/0000-0003-2621-8860 and Laurent, ThibaultORCID: https://orcid.org/0000-0001-7487-7671 (2026) Robust Frontier and Efficiency Analysis with frontiles. TSE Working Paper, n. 26-1731, Toulouse

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Abstract

This chapter discusses the current state of development of robust measures for evaluating firms’ production performance, focusing on two prominent approaches: (i) partial order-m frontiers and related efficiency scores based on probability-weighted moments, and (ii) their competing order-α counterparts, which rely on quantiles. It provides a structured overview of the original concepts and their recently introduced robustified versions, analyzing their strengths and weaknesses in terms of axiomatic properties, estimation methods, and robustness. The frontiles package offers various functions for computing both order-α and order-m frontiers and efficiency scores, including their robustified analogs, in the general setting with multiple inputs and outputs. It supports different performance measurement directions, namely input, output and hyperbolic orientations. Additionally, frontiles includes procedures for inference and robustness assessment, notably through confidence intervals, gross-error sensitivity and breakdown points. It also provides diagnostic checks to assess the presence of outliers in the data and, accordingly, to guide the choice of suitable trimming levels. It further enables the visualization of robust surface estimators in three-dimensional settings involving two inputs and one output. The use of this package is illustrated with a number of empirical applications.