A Gram–Schmidt process based approach for improving DEA discrimination in the presence of large dimensionality of data set

The objective of this paper is to deal with the performance evaluation problem in the presence of large dimensionality of data set, in which there exist multiple correlations among the original variables. Firstly, this paper analyzes the weakness of principal component analysis (PCA), and introduces a maximum variance method to reduce data dimension via Gram–Schmidt process, through which the corresponding transformed variables (Schmidt variables) can be obtained. And at the same time, a measure of investigating the cumulative variation information for selected Schmidt variables is described. Then based upon the chosen Schmidt variables, a new modified DEA approach with a natural assurance region (AR) is presented. In the developed DEA approach, the selected Schmidt variables are treated as outputs. The proposed approach will be then contrasted with the traditional CCR DEA model and the DEA model using principal components obtained from PCA with simulated data, and it is also applied to real world data set that characterizes economic performance of 31 provinces or cities in China.