统计研究 ›› 2012, Vol. 29 ›› Issue (7): 91-95.

• 论文 • 上一篇    下一篇

基于正态分布点值化的区间主成分评价法及应用

陈骥 王炳兴   

  • 出版日期:2012-07-15 发布日期:2012-07-13

Interval Principal Component Analysis based on the Point-Estimation of Normal Distribution and its Application

Chen Ji & Wang Bingxing   

  • Online:2012-07-15 Published:2012-07-13

摘要: 针对区间数据点值化过程中所存在的“代表性不足”的缺陷,提出了基于正态分布的点值化方法并将之应用于区间主成分评价法。通过与基于中心点值化的区间主成分法的比较,得到三个主要结论:第一,基于正态分布的点值化方法能将各样品的点值化结果导向指标均值,而非区间值的中心点;第二,基于正态分布的点值化结果增加了数据信息量;第三,基于正态分布点值化的区间主成分评价法提高了数据降维效果,具有更好的因子命名能力。应用结果表明,在考虑正态分布情况下,对区间数据的点值化处理方法具有较好的效果,基于正态分布点值化的方法可推广至基于区间数的评价和决策问题。

关键词: 区间值变量, 综合评价, 主成分分析, 正态分布

Abstract: Focusing on the defects of lacking in representation in the process of convert the interval-valued data into point-data, this paper proposes a new method based on normal distribution and applies it into interval-principal component analysis. There are three advantages compared with centers method of principal component analysis for interval-valued data. Firstly, the method of point estimation based on normal distribution can make the point estimation of cases to the mean of index, rather than the midpoint of interval-valued data. Secondly, the data’s point estimation based on normal distribution increases information quantity. Thirdly, interval principal component analysis based on the point estimation of normal distribution enhances the effect of data reduction, and has a better ability to name the factors. The result indicates that the new method can be extended to other methods of comprehensive evaluation or decision making based on interval-valued data.

Key words: Interval-valued Data, Comprehensive Evaluation, Principal Component Analysis, Normal Distribution