主灵敏度矢量的快速最小中位方差估计方法  

Fast Least Median of Squares Based on Principal Sensitivity Vectors

作　　者：张华[1] 梁逸曾[2] 许青松[3] 周其伟[4] 

机构地区：[1]湖南大学化学计量学与传感技术研究所,长沙410082 [2]中南大学化学化工学院,长沙410083 [3]湖南大学数学与计量经济学院,长沙410082 [4]湖南省药品检验所,长沙410001

出　　处：《计算机与应用化学》2001年第4期319-323,共5页Computers and Applied Chemistry

基　　金：国家自然科学基金重点课题资助 (批准号 :2 9735 15 0 )

摘　　要：杠杆点存在时的稳健多元校正 ,是分析化学中有意义的课题。本文基于最小中位方差估计法机理 ,通过定义主灵敏度矢量来删除奇异点 ,进行迭代运算 ,获得一初始估计 ,检验后获得最终解答。本方法对仿真实验及实际多组分药物的分析均取得了满意结果 ,有效地解决了回归问题中强杠杆点的掩蔽效应 。A fast estimator for the large regression problems is proposed based on the mechanism of least median of squares (LSE) in this work. The main idea of the procedure is to use a robust scale for evaluating a set of possible solutions.These solutions are determined by applying LSE to subsets of samples in which subsets of potentially outlier observations have been deleted by the principal sensitivity vectors. The procedure contains two stages. The first stage is an iterative procedure. In each iteration, a robust estimate is obtained based on the LSE by deleting the possible outliers which appear as the extreme points in the principal sensitivity vectors. The iterations continue until convergence.In the second stage, the points deleted are tested one by one using the studentized residuals. The final estimate is computed by LSE using the cleaned samples. The most attractive advantage of this approach is its strong avoiding the masking effects of the leverage points. The results from both computer simulation and two real data sets showed that the procedure is a prospective robust regression method for QSAR and multivariate calibration in chemometrics.

关 键 词：奇异点 掩蔽效应 主灵敏度矢量 分析化学 最小中位方差估计法 杠杆点 稳健多元校正 

分 类 号：O65-37[理学—分析化学]