ASYMPTOTICS AND CONSISTENT BOOTSTRAPS FOR DEA ESTIMATORS IN NONPARAMETRIC FRONTIER MODELS
推导了可变规模报酬下DEA估计量的渐近分布，并证明两种自助法（子抽样和平滑自助法）的一致性，为效率推断提供可靠方法。
Nonparametric data envelopment analysis (DEA) estimators based on linear programming methods have been widely applied in analyses of productive efficiency. The distributions of these estimators remain unknown except in the simple case of one input and one output, and previous bootstrap methods proposed for inference have not been proved consistent, making inference doubtful. This paper derives the asymptotic distribution of DEA estimators under variable returns to scale. This result is used to prove consistency of two different bootstrap procedures (one based on subsampling, the other based on smoothing). The smooth bootstrap requires smoothing the irregularly bounded density of inputs and outputs and smoothing the DEA frontier estimate. Both bootstrap procedures allow for dependence of the inefficiency process on output levels and the mix of inputs in the case of input-oriented measures, or on input levels and the mix of outputs in the case of output-oriented measures.