一种新的基于回归分析的异常值检测  

Outliers Detection of a New Method Based on Regression Analysis

作　　者：尚华[1] 张贝贝[1] 纪宏[1] 

机构地区：[1]首都经济贸易大学统计学院,北京100070

出　　处：《河南大学学报（自然科学版）》2015年第6期635-639,共5页Journal of Henan University:Natural Science

基　　金：国家自然科学基金数学天元基金(11426159);北京市教育委员会社会科学研究计划项目(SM201310038007)

摘　　要：异常值检测是当前数据分析中的一个重要研究领域.模型中的异常值会直接影响建模、参数的估计、预测等问题.回归分析是应用极其广泛的数据分析方法之一,本文针对回归分析中的异常值检测进行了研究.该方法基于均值转移模型,根据异常值对残差平方和的影响关系构造一个新的异常值判断准则的统计量,并给出了估计异常值大小的公式.本文进行了大量的模拟实验和实例分析,与传统方法相比,结果表明该方法是有效的.Outliers detection is an important research field in the current data analysis.Outliers in the data will affect the modeling,estimating parameters,forecasting and other issues directly.Regression analysis is one of the most widespread application of data analysis methods.We suggest a new method for outliers detection based on regression analysis in this article.Mean-shift model is considered in this paper.A new statistic method detecting outliers according to the relationship between sum of squares for error（SSE）and outliers is proposed.Moreover,the method of estimating the size of those outliers is given.The approach is more effective to outliers compared with traditional methods,which is illustrated with a large number of simulation studies as well as real data.

关 键 词：回归分析 异常值 最小二乘估计(OLS) 残差平方和(SSE) 

分 类 号：O212.1[理学—概率论与数理统计]