In data envelopment analysis (DEA), the curse of dimensionality problem may jeopardize the accuracy or even the relevance of results when there is a relatively large dimension of inputs and outputs, even for relatively large samples. Recently, a machine learning approach based on the least absolute shrinkage and selection operator (LASSO) for variable selection was combined with sign-constrained convex nonparametric least squares (SCNLS, a special case of DEA), and dubbed as LASSO-SCNLS, as a way to circumvent the curse of dimensionality problem. In this paper, we revisit this interesting approach, by considering various data generating processes. We also explore a more advanced version of LASSO, the so-called elastic net (EN) approach, adapt it to DEA and propose the EN-DEA. Our Monte Carlo simulations provide additional and to some extent, new evidence and conclusions. In particular, we find that none of the considered approaches clearly dominate the others. To circumvent the curse of dimensionality of DEA in the context of big wide data, we also propose a simplified two-step approach which we call LASSO+DEA. We find that the proposed simplified approach could be more useful than the existing more sophisticated approaches for reducing very large dimensions into sparser, more parsimonious DEA models that attain greater discriminatory power and suffer less from the curse of dimensionality.