Production Frontier Estimation via Additive Regression Splines and Relaxed Support Vector Regression

This paper introduces two approaches for estimating the production frontier, which are based on the additive regression splines and the Relaxed Support Vector Regression (RSVR). In the field of production frontier estimation, recent studies have widely adopted machine learning techniques to improve traditional estimation methods. Among them, the Support Vector Frontier (SVF) and the Convexified SVF (CSVF) have solved the overfitting problems found in Free Disposal Hull (FDH) and Data Envelopment Analysis (DEA), and they are improvements of the SVR technique. However, SVF and CSVF suffer from the curse of dimensionality and are highly sensitive to outliers in actual data. Moreover, there is no specific form of the estimation for CSVF. To address these limitations, we proposed two novel approaches termed Relaxed Additive SVF (RASVF) and Relaxed Additive convex SVF (RAcSVF). They are, respectively, extensions of SVF and CSVF and also follow the corresponding axioms in production theory. Finally, experiments conducted on the synthetic dataset show that the proposed approaches outperform FDH, DEA, SVF, and CSVF in handling situations involving multiple inputs or outliers. Meanwhile, our approaches exhibit a shorter runtime compared to SVF and CSVF.