正交最小二乘法及其在分析化学中的应用

介绍了一种线性模型参数回归分析方法-正交最小二乘法，并以电子探针微区分析技术分析环境样品的数据为例，对正交最小二乘法和经典最小二乘法的结果进行了详细比较。数据处理结果表明，当变自量和因变量都同时存在测量误差时（或自变量的测量误差与因变量的测量误差相比不能忽略时），正交最小二乘法获得的回归系数优于经典最小二乘法。对正交最小二乘法中的线性模型能解释的方差与经典最小二乘法中的相关系数的关系也进行了讨论。

Orthogonal Least Squares Method and Its Application in Analytical Chemistry

A linear parameter estimation technique, the orthogonal least squares (OLS) method, is presented in this paper. The results obtained by the OLS method are compared in detail with those by classical least squares (CLS) method based on electron probe microanalysis data sets which used to estimate the ratio of K to Cl and S intensity for elemental speciation analysis. Our experimental data sets validate that when independent and dependent variables are corrupted by noise the estimates obtained with the OLS method are superior to those with the CLS method. The reliability of the parameter from OLS can be evaluated by the variance explained by the model (VEM). The closer the VEM value to unity, the better the quality of regression analysis. The relationship between the VEM, an index for evaluating the reliability of parameter in OLS, and R squared in CLS is also discussed.