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。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。
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.
出处
《统计研究》
CSSCI
北大核心
2012年第7期91-95,共5页
Statistical Research
基金
国家社科基金项目"基于区间信息的综合评价问题研究"(09BTJ001)
浙江省自然科学基金项目"产业链视角下的浙江省纺织行业景气评价与预警体系研究--基于区间化不确定信息的分析"(Y6110777)
"基于区间信息的专业市场景气波动测度与预警体系研究"(Q12G030068)
浙江省高校人文社科重点研究基地(浙江工商大学统计学)的资助
关键词
区间值变量
综合评价
主成分分析
正态分布
Interval-valued Data
Comprehensive Evaluation
Principal Component Analysis
Normal Distribution