基于FDOD度量的多维系统优化中的强相关问题  

A Research on Multicollinearity in Multidimensional System Optimization Based on FDOD Measurement

作　　者：韩亚娟[1] 

机构地区：[1]上海大学管理学院,上海200444

出　　处：《工业工程》2013年第5期79-84,95,共7页Industrial Engineering Journal

基　　金：高等学校博士学科点专项科研基金(新教师类)资助项目(20093108120023);国家自然科学基金(青年基金)资助项目(71101086)

摘　　要：强相关问题是多维系统优化降维分析中的一个常见问题。多维系统强相关问题的存在,使得衡量样本异常程度的综合评价指标——马氏距离难以计算或很不准确,进而给基于马氏距离函数进行的多维系统优化与诊断分析带来困扰。田口试图通过改进马氏距离函数来解决强相关问题,提出了马氏田口施密特正交化法和伴随矩阵法,然而这2种方法本身存在无法克服的缺陷。基于多重信息源信息离散性(FDOD)度量的特性,提出用FDOD度量代替马氏距离函数来衡量多维系统样本的异常程度,并将FDOD度量与田口方法结合进行多维系统优化降维与样本诊断分析,彻底解决多维系统优化中的强相关问题。通过对西班牙银行在金融危机时的稳健性分析,进一步证实了所提出方法的有效性。Due to the multicollinearity, it is difficult to accurately calculate the Mahalanobis distance, which is puzzling in multidimensional system analysis. Gram-Schmidt method and adjoint matrix method of MTS, put forward by Genichi Taguchi, are used to solve muhicollinearity problems by improving Mahal- anobis distance function. However, both of them have some insuperable defects. The function of degree of disagreement （FDOD） measurement, a method based on entropy, is adopted to measure the degree of ab- normality of multidimensional observations instead of Mahalanobis distance function. Also, FDOD meas- urement and Taguchi method are integrated for multidimensional system optimization and dimension reduc- tion, which thoroughly solve muhicollinearity problems. Cases of Spanish banks in financial crisis are ana- lyzed to illustrate the effectiveness of the proposed method.

关 键 词：多维系统 强相关问题 FDOD度量 田口方法 

分 类 号：F406.2[经济管理—产业经济]