Super-efficiency based on a modified directional distance function

The problem of infeasibility arises in conventional radial super-efficiency data envelopment analysis (DEA) models under variable returns to scale (VRS). To tackle this issue, a Nerlove–Luenberger (N–L) measure of super-efficiency is developed based on a directional distance function. Although this N–L super-efficiency model does not suffer infeasibility problem as in the conventional radial super-efficiency DEA models, it can produce an infeasible solution in two special situations. The current paper proposes to modify the directional distance function by selecting proper feasible reference bundles so that the resulting N–L measure of super-efficiency is always feasible. As a result, our modified VRS super-efficiency model successfully addresses the infeasibility issues occurring either in conventional VRS models or the N–L super-efficiency model. Numerical examples are used to demonstrate our approach and compare results obtained from various super-efficiency measures.     

A slacks-based measure of super-efficiency in data envelopment analysis: An alternative approach

The current paper proposes a slack-based version of the Super SBM, which is an alternative super-efficiency model for the SBM proposed by Tone. Our two-stage approach provides the same super-efficiency score as that obtained by the Super SBM model when the evaluated DMU is efficient and yields the same efficiency score as that obtained by the SBM model when the evaluated DMU is inefficient. The projection identified by the Super SBM model may not be strongly Pareto efficient; however, the projection identified from our approach is strongly Pareto efficient.     

An integrated model for slack-based measure of super-efficiency in additive DEA

As a non-radial approach, a super-efficiency model, Super SBM, was proposed by Tone [15] to rank efficient DMUs. Du et al. [7] extends the Super SBM model to the additive (slacks-based) DEA model. To obtain the super-efficiencies of the DMUs, one needs to identify the efficient DMUs first and then apply the additive super-efficiency model to those efficient DMUs. In this paper, we propose an integrated model so that the efficiencies of the inefficient DMUs and the super-efficiencies of the efficient DMUs can be obtained by a single model. The efficiency scores obtained by our integrated model are the same as those obtained by Du et al. [7] and the additive DEA model.     

A novel weighted likelihood estimation with empirical Bayes flavor

We propose a novel approach to estimation, where a set of estimators of a parameter is combined into a weighted average to produce the final estimator. The weights are chosen to be proportional to the likelihood evaluated at the estimators. We investigate the method for a set of estimators obtained by using the maximum likelihood principle applied to each individual observation. The method can be viewed as a Bayesian approach with a data-driven prior distribution. We provide several examples illustrating the new method and argue for its consistency, asymptotic normality, and efficiency. We also conduct simulation studies to assess the performance of the estimators. This straightforward methodology produces consistent estimators comparable with those obtained by the maximum likelihood method. The method also approximates the distribution of the estimator through the “posterior” distribution.     

Consistency and asymptotic distribution of the Theil–Sen estimator

In this paper, we obtain the strong consistency and asymptotic distribution of the Theil–Sen estimator in simple linear regression models with arbitrary error distributions. We show that the Theil–Sen estimator is super-efficient when the error distribution is discontinuous and that its asymptotic distribution may or may not be normal when the error distribution is continuous. We give an example in which the Theil–Sen estimator is not asymptotically normal. A small simulation study is conducted to confirm the super-efficiency and the non-normality of the asymptotic distribution.     

空间效应视角下的中国省域工业技术创新效率收敛性研究

本文基于2009—2018年我国30个省份的面板数据,构建非导向、非径向且规模报酬可变的窗口MinDS超效率模型测度各省份的工业技术创新效率,采用全局莫兰指数检验省域工业技术创新效率的空间相关性,然后使用变异系数、建立空间计量模型进行σ收敛、β收敛分析。研究结果表明:我国省际工业技术创新效率的均值为0.7499,东部、中部、西部三大区域差异较明显,依次降低;10年期间东部、中部的工业技术创新效率有降有升,而西部则基本上稳定上升;省域工业技术创新效率的空间分布呈现显著的正向空间相关;全国与分区域均未出现σ收敛,但同时存在绝对β收敛与条件β收敛。本研究明晰了各省份的工业技术创新效率及其收敛性,为缩小工业技术创新效率区域差距、促进工业经济高质量发展提供现实依据与理论借鉴。