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现有的对DEA模型中出现负值的研究,主要是针对一些简单的半导向型、径向的模型研究,但是对于复杂的模型,大多是将负值变量先行处理为正值后,再代入模型,丧失了原有的数据结构,导致模型的准确性和可靠性遭到质疑,尤其是Hybrid DEA模型,包含了径向与非径向、无导向的因素,目前尚无对负值情况的研究。因此,本文以半导向模型CCR为基础,经过数学推导,得到一系列无导向、非径向的数学模型,并将Emrouznejad et al.的负值处理规则应用到这些模型,从而得到能处理负值情况的无导向径向模型(NORM-VRS DEA)和无导向非径向模型(NOM-VRS DEA),进而对其数学模型进行了深入的研究,推导得出相关引理与结论,最终解决了Hybrid DEA模型带有负值情况的问题。随后,利用开发的模型对中国规范型证券公司的经营效率进行了实证分析,验证了模型的实际有效性以及所推导出的引理和结论是否正确,发现了与原有Hybrid DEA理论的一些不相符之处,并对其原因进行了简单分析。
Existing studies on the negative values of DEA model mainly focus on some simple semi-oriented and radial model studies. However, for complex models, most of the negative variables are treated as positive first and then substituted into Model, the original data structure is lost, which leads to the accuracy and reliability of the model being questioned. In particular, the Hybrid DEA model includes both radial and non-radial and non-oriented factors. There is no negative the study. Therefore, based on the semidirectional model CCR, a series of non-oriented and non-radial mathematical models are obtained through mathematical derivation, and the negative rule of Emrouznejad et al. Is applied to these models to obtain the negative value (NORM-VRS DEA) and NOM-VRS DEA, and further study its mathematical model, derive the relevant lemma and conclusion, finally solve the problem Hybrid DEA Model with Negative Value Problems. Subsequently, the paper uses the developed model to make an empirical analysis of the operating efficiency of China’s normative securities companies, verifying the actual validity of the model and whether the derived lemmas and conclusions are correct or not, finding some differences from the original Hybrid DEA theory Coincidence, and the reason for a simple analysis.