DEA for big wide data based on regularization approaches: An application to energy efficiency analysis

In data envelopment analysis (DEA), the problem of the curse of dimensionality is a tough nut to crack when a relatively large dimension of inputs and outputs exists, especially in the context of big wide data. To solve the problem of the curse of dimensionality, the existing literature has proposed several LASSO-type methods combining LASSO and adaptive LASSO (ALASSO) with DEA or sign-constrained convex nonparametric least squares (SCNLS), e.g., LASSO＋DEA, ALASSO＋DEA, and ALASSO-SCNLS. In this paper, we propose another hybrid approach by combining the non-negative least squares (NNLS) regression with DEA, and call it NNLS＋DEA. Compared to the existing LASSO-type methods, NNLS＋DEA has a simpler penalty function for regularization, does not have a tuning parameter, and does not require cross-validation. When comparing the performance of NNLS＋DEA with the LASSO-type methods, our Monte Carlo simulations show that: (1) LASSO＋DEA shows better performance compared to ALASSO＋DEA and ALASSO-SCNLS despite the merit of consistent variable selection of the ALASSO; (2) NNLS＋DEA shows slightly better performance than LASSO＋DEA for relatively small sample sizes or considerably large dimensions; (3) NNLS＋DEA clearly dominates LASSO＋DEA in the computing time, especially for large dimensions. Finally, we also provide an empirical illustration, applying NNLS＋DEA to estimate efficiency with real data for Swedish electricity distribution system operators and for Chinese provincial energy data.