WHEN BIAS KILLS THE VARIANCE: CENTRAL LIMIT THEOREMS FOR DEA AND FDH EFFICIENCY SCORES
证明标准中心极限定理不适用于DEA和FDH效率得分的均值，因为个体得分的偏差大于方差或协方差，并开发了新的中心极限定理用于均值效率水平的推断，通过蒙特卡洛实验验证其有效性。
Data envelopment analysis (DEA) and free disposal hull (FDH) estimators are widely used to estimate efficiencies of production units. In applications, both efficiency scores for individual units as well as average efficiency scores are typically reported. While several bootstrap methods have been developed for making inference about the efficiencies of individual units, until now no methods have existed for making inference about mean efficiency levels. This paper shows that standard central limit theorems do not apply in the case of means of DEA or FDH efficiency scores due to the bias of the individual scores, which is of larger order than either the variance or covariances among individual scores. The main difficulty comes from the fact that such statistics depend on efficiency estimators evaluated at random points. Here, new central limit theorems are developed for means of DEA and FDH scores, and their efficacy for inference about mean efficiency levels is examined via Monte Carlo experiments.