Technical efficiency estimation using adaptive constrained enveloping splines
The accurate measurement of technical efficiency represents a central goal in both theoretical and applied economic analysis, as it allows organizations, industries, and policymakers to assess performance, allocate resources efficiently, and identify areas for improvement. Among the various tools de...
| Autor: | |
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| Formato: | tesis doctoral |
| Fecha de publicación: | 2026 |
| País: | España |
| Recursos: | Universidad Miguel Hernández de Elche |
| Repositorio: | REDIUMH. Depósito Digital de la UMH |
| OAI Identifier: | oai:dnet:rediumh_____::68edda1c4ada8d1a94e3ce1b00cd1b31 |
| Acesso em linha: | https://hdl.handle.net/11000/39842 |
| Access Level: | acceso abierto |
| Palavra-chave: | Data Envelopment Analysis (DEA) production frontier estimation technical efficiency Adaptive Constrained Enveloping Splines (ACES) CDU::3 - Ciencias sociales::33 - Economía CDU::5 - Ciencias puras y naturales::51 - Matemáticas CDU::0 - Generalidades.::04 - Ciencia y tecnología de los ordenadores. Informática. |
| Resumo: | The accurate measurement of technical efficiency represents a central goal in both theoretical and applied economic analysis, as it allows organizations, industries, and policymakers to assess performance, allocate resources efficiently, and identify areas for improvement. Among the various tools developed for this purpose, Data Envelopment Analysis (DEA) has emerged as a predominant non-parametric methodology, widely adopted for its conceptual simplicity and operational flexibility. DEA constructs a production frontier enveloping observed data without requiring prior specification of a functional form, making it suitable for diverse applications across sectors such as education, healthcare or banking. However, despite its widespread use, DEA presents several important methodological limitations that hinder its broader applicability and accuracy in practice. Chief among these are issues related to overfitting, particularly when the number of inputs and outputs is large relative to the sample size, leading to overly optimistic efficiency estimates. Additionally, DEA lacks a natural framework for statistical inference, preventing the derivation of confidence intervals or hypothesis testing without relying on complex and computationally intensive bootstrap procedures. A further critical limitation lies in the absence of systematic guidance for variable selection, which makes the analysis highly sensitive to the analyst’s choices and susceptible to distortions from irrelevant or redundant variables. These challenges become even more pronounced in high-dimensional data environments, where relationships among variables tend to be complex and nonlinear, often exceeding the capacity of DEA to accurately capture the underlying production structure. The thesis presents a unified family of techniques for estimating production frontiers, designed to address key limitations of traditional DEA, such as overfitting, limited robustness, and challenges in high-dimensional settings. This family includes three complementary methods: Adaptive Constrained Enveloping Splines (ACES), which offers a flexible estimator of technical efficiency; Random Forest-ACES (RF-ACES), which enhances robustness through ensemble learning; and Quick-ACES (Q-ACES), which focuses on computational efficiency for large-scale applications. Each method addresses different empirical needs, enabling researchers to select the most appropriate approach based on the characteristics of the data. At the core of this framework lies ACES, a method built upon an adapted version of Multivariate Adaptive Regression Splines (MARS), specifically tailored for production frontier estimation. ACES integrates essential shape constraints—monotonicity and concavity—into a spline-based, non-parametric regression model, ensuring consistency with microeconomic theory. The estimation is formulated as a constrained optimization problem and follows a two-stage procedure: first, a rich set of candidate basis functions is generated through forward selection; then, the model is refined via backward elimination guided by generalized cross-validation. This process yields a flexible estimator capable of modeling complex, nonlinear input–output relationships while avoiding the overfitting commonly associated with DEA. A key strength of ACES is its ability to remain fully deterministic while achieving strong generalization beyond the observed sample—representing a major advance over traditional enveloping methods. To improve robustness and mitigate the sensitivity of spline-based models to local data configurations, the thesis extends ACES into an ensemble version named RF-ACES. This method builds on the principles of bagging and random feature selection, inspired by the Random Forest algorithm. In RF-ACES, multiple ACES models are trained on bootstrap samples of the original dataset using randomly selected subsets of inputs at each iteration. The resulting estimators are aggregated to form a final predictor that is significantly more stable and less sensitive to random noise. An important strength of RF-ACES lies in its ability to provide internal variable importance measures, which can be used to guide dimensionality reduction and identify the most influential inputs. This makes it particularly effective in high-dimensional settings or when irrelevant variables are suspected to distort the estimation. Nevertheless, this increase in robustness comes at the cost of computational burden, since multiple constrained estimations must be performed and aggregated. Finally, to address computational limitations and ensure scalability to large datasets or timesensitive applications, the thesis proposes a third member of the family: Q-ACES. This accelerated variant introduces a set of heuristic strategies designed to reduce the computational burden of the estimation process without compromising the theoretical principles underlying ACES. These strategies include input pre-selection based on correlation analysis, reduction of knot sets through neighborhood analysis derived from DEA projections, and adaptive filtering of candidate basis functions during the forward selection phase. In addition to these mechanisms, Q-ACES incorporates a new automated procedure for variable selection, which serves as an alternative to the Random Forest-based relevance assessment implemented in RF-ACES. This procedure allows for efficient identification of the most influential inputs while preserving the model’s accuracy. As a result, Q-ACES achieves substantial improvements in execution time and memory efficiency, enabling the application of shape-constrained frontier estimation in large-scale scenarios where the original ACES framework would be computationally impractical. Together, these three methods—ACES, RF-ACES, and Q-ACES—constitute a flexible and modular toolkit for technical efficiency analysis. Analysts can select the most appropriate variant depending on the size and complexity of the dataset, the tolerance for approximation, and the need for robustness. This family-based approach allows practitioners to move beyond the static and sample-dependent nature of DEA, adopting frontier estimators that are not only theoretically grounded but also adaptive to modern data analysis challenges. The proposed methodologies have been extensively validated through hundreds of simulation experiments, covering a wide range of scenarios with varying dimensionality, noise levels, and production structures. Results consistently confirm the competitiveness of ACES and its variants against established techniques such as DEA, Corrected Concave Non-parametric Least Squares (CCNLS), Stochastic Non-Smooth Envelopment of Data (StoNED), and Bootstrap DEA, often yielding more accurate and stable estimates. Furthermore, the thesis offers practical guidance on how to configure and tune ACES in different empirical contexts, helping researchers make informed decisions to maximize performance and reliability in their applications. |
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