Support Vector Frontiers with kernel splines

Abstract

Among recent methodological proposals for efficiency measurement, machine learning methods are playing an important role, particularly in the reduction of overfitting in classical statistical methods. In particular, Support Vector Frontiers (SVF) is a method which adapts Support Vector Regression (SVR) to the estimation of production technologies through stepwise frontiers. The SVF estimator is convexified in a second stage to deal with convex technologies. In this paper, we propose SVF-Splines, an extension of SVF for the estimation of efficiency in multi-input multi-output production processes which uses a transformation function generating linear splines to directly estimate convex production technologies. The proposed methodology reduces the computational complexity of the original SVF and does not require a two-step estimation process to obtain convex production technologies. A simulated experiment comparing SVF-Splines with standard DEA and (convexified) SVF indicates better performance of the proposed methodology, with improvements of up to 95 % in mean squared error when compared with DEA. The computational advantages of SVF-Splines are also observed, with runtime over 70 times faster than SVF in certain scenarios, with better scaling as the size of the problem increases. Finally, an empirical illustration is provided where SVF-Splines is calculated with respect to various typical technical efficiency measures of the literature.