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中文摘要：
首先分别构建了考虑期望产出和非期望产出的生产函数，进行环境效率DEA评价方法的凸非参数最小二乘估计，提出当参数αi1,βi1,αi2,βi2的估计值给定时，可以得到f和g的显性表达式，然后利用考虑非期望产出的DEA及凸非参数最小二乘CNLSUO，可以求得拟合曲线之间的数量关系，即对于每个DMU的实际投入，CNLSUO法得到的产出拟合值不大于DEA法得到的产出拟合值．实证分析表明，考虑期望产出和非期望产出的DEA估计效果较好．包括考虑非期望产出DEA的非参数最小二乘估计在内的环境效率评价方法的统计属性分析，势必会拓展DEA统计属性研究的范畴，推动统计学与运筹学的进一步融合与发展．
英文摘要：
Production function of the expected outputs and undesirable outputs are constructed in this article firstly, and then non-convex nonparametric least squares estimation considering the undesirable outputs is studied. When αi1,βi1,αi2,βi2, are given, explicit expression of f and g can be obtained. According to DEA considering undesirable outputs and CNLSUO, relationship between the two fitting curves can be calculated. For the actual outputs of each firm, the estimation of CNLSUO is never larger than that of DEA. Empirical analysis shows that the DEA estimation considering the desirable and undesirable outputs is good. The analysis of statistical properties of methods for environmental efficiency evaluation, including least squares estimation of DEA considered undesirable outputs is bound to expand the scope of non-parameter statistical properties of DEA, which promote the further integration and development of statistics and operations.
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