多元统计描述中随机误差与变量空间角的关系  

The relationship between the error and subspace angles in linear multivariate analysis

作　　者：姚志湘[1] 粟晖[1] 

机构地区：[1]广西工学院生物与化学工程系,柳州545006

出　　处：《中国科学：化学》2010年第10期1564-1570,共7页SCIENTIA SINICA Chimica

基　　金：广西自然科学基金项目(桂科自0832064);广西教育厅科学基金项目(200708MS067)资助

摘　　要：多元分析的误差传递需要一种简单、准确、数值化的表达方法.向量空间中,线性多元混合信号的随机误差可表述成真值子空间中随机向量的表现;由体系多元变量对应的向量构成的真值子空间中,被关注向量和其他向量子空间的空间角θ是描述多元体系的重要参数.如果被关注向量和其他向量子空间关系确定,体系总体误差呈正态分布,那么,被关注向量上误差也是正态分布,其多元统计分析结果的标准差与体系误差标准差的比值为1/(2·sin(θ/2),结论在构造算例和邻、间、对苯二酚混合体系的紫外光度分析中得到验证.A similarly direct numerical assessment for error propagation has considerable appeal in multivariate analysis. That the whole measurement signals include the linear mixed signals and random error can be described as two parts in vector space, one is true value subspace which is spanned by variables of system and the other is random space, the angle （8） between the attention vector and the subspace spanned by others vectors is a important parameter. If the true value subspace is determinate and random error is normal distribution, then the error on the attention vector also is normal distribution. The ratio between the two standard deviations （one deviation is error on the attention vector of multivariate analysis output and another is whole system random error） is 1/（2.sin（θ/2））. The conclusion has been authenticated by a constructed dataset and a spectrophotometric example which is UV spectrums mixed by catechol, resorcinol and hydroquinone.

关 键 词：多元分析 误差 向量空间 空间角 多元校正 

分 类 号：O651[理学—分析化学]