线性模型基于M估计的统计诊断与影响分析
M Estimators and Influence Diagnostics in Linear Models

作者: 姜 荣 , 钱伟民 :同济大学应用数学系,上海;

关键词: 数据删除模型均值漂移模型局部影响M估计Cook距离 Case-Deletion Model Mean-Shift Outlier Model Local Influence M Estimate Cook Distance

摘要:

为了克服实际观测数据与既定模型之间可能存在的较大偏离,目前有两种常用的处理方法:稳健统计与统计诊断。M方法是最重要的稳健统计之一,也是线性回归分析中是最受重视和研究成果最多的方法之一。所以本文结合M估计方法分析数据的统计诊断,从而得到异常点或强影响点。本文给出了参数估计偏离的表达式及几个诊断统计量,最后通过两个实例验证了本文所提方法的可行性。

Abstract:

 In order to overcome the large deviation between the actual observed data and established models. There are two common methods: the robust estimation and statistical diagnostics. M estimator is a robust es- timation, it is the method which got the most attention and research results in linear regression. Therefore, in- fluence diagnostics and M estimator are used to judge the impact of outliers or strong influence points in this paper. Moreover, the expression of parameter estimation deviate and diagnostic statistics are given. Finally, the proposed methods are applied to two data sets.

 

文章引用: 姜 荣 , 钱伟民 (2012) 线性模型基于M估计的统计诊断与影响分析。 统计学与应用, 1, 31-36. doi: 10.12677/SA.2012.12007

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