The Applications And Relative Efficiency Analysis Of Multivariate Statistical Methods In Comprehensive Evaluation

Abstract:Comprehensive evaluation is a procedure that determines the order of every subject we evaluate in whole in the form quantity by collecting all information of the subjects. Multivariate statistical analysis is the important methods for integrated data processing in comprehensive evaluation which is involved in many fields such as society, science, etc. In this paper, we focus on the principal component analysis and a statistical methods based on the principal component analysis.Different evaluation models lead to different conclusions. In this paper, for the non-conformance of the conclusions of the evaluation models,we build three indicators:the confidence,the similarity and the dispersion to measure the relative efficiency of the model.As an important statistical method, not only PCA transform the indicator variables into the composite indicators which not relevant together, and the composite indicators have a good property:a few of composites can reflect the informations of all the primitive variables and it plays the role of dimension reduction. PCA is a method of dimension reduction overall. The paper introduces a new method which reduces dimensions gradually from locale to the whole---Binary Tree Dimension Reduction(BTDR):The two variables having strongest correlation produce a new variable, and the new variable replace the two variables. This dimension reduction process would be executed circularly until the precision demanded obtained. The process can be described a Binary Tree. The paper combines the thoughts of the partial dimension reduction of BTDR and the whole dimension reduction of PCA:once for each partial dimension reduction, it conducts a general dimension reduction. By comparing the relative effectiveness of the models, we can find relatively reasonably accurate models to reduce the losses of the informationsBase on the2012economic indicators of the Changsha above-scale enterprises by industries, we analyze the data by the models of the paper to evaluate and measure the relative efficiency of the models. And through the relative efficiency, we find the relative efficiency of the model of coefficient of variation, the model of the cumulative contribution of variance, factor analysis and KPCA descend by order. While exploring the BTDR, the relative efficiency is highest when setting three-step partial dimension reduction and then setting the overall dimension reduction.