| 粗差探测与识别统计检验量的比较分析 |
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| 引用本文： | 郭建锋,赵俊.粗差探测与识别统计检验量的比较分析[J].测绘学报,2012,41(1):14-0. |
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| 作者姓名： | 郭建锋 赵俊 |
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| 作者单位： | 信息工程大学 |
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| 基金项目： | 国家自然科学基金，国家杰出青年科学基金 |
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| 摘 要： | LS估计对粗差非常敏感。在粗差的探测与识别理论体系中,通常采用正态检验、学生氏t检验以及τ检验等,笔者对此进行比较分析。标准化局部敏感度指标与标准化LS残差均可用来作正态检验,但研究表明,当观测量相关时,前者的检验功效大于后者。先验单位权方差因子未知时,可依据内部学生化残差及外部学生化残差分别进行τ检验和学生氏t检验。...
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| 关 键 词： | 粗差 敏感度分析 高斯正态检验 学生氏t检验 τ检验 |
| 收稿时间： | 2010-12-31 |
| 修稿时间： | 2011-06-03 |
Comparative Analysis of Statistical Tests Used for Detection and Identification of Outliers |
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| GUO Jianfeng,ZHAO Jun.Comparative Analysis of Statistical Tests Used for Detection and Identification of Outliers[J].Acta Geodaetica et Cartographica Sinica,2012,41(1):14-0. |
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| Authors: | GUO Jianfeng ZHAO Jun |
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| Institution: | 1.Institute of Science,Information Engineering University,Zhengzhou 450001,China;2.Institute of Geodesy and Geophysics,Chinese Academy of Sciences,Wuhan 430077,China |
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| Abstract: | The least-squares(LS) adjustment approach is very susceptive to outliers.A comparative analysis of statistical tests used for detection and identification of outliers,including Gaussian normal test,Tau test and Student’s t-test,were addressed in details.Both the standardized local sensitivity indicator and the standardized LS residual can be served as Gaussian normal test statistics for outlier detection.However,the former is superior to the latter one for correlated observations in the sense of detection power.When the variance factor is not known,the internally Studentized residual and externally Studentized residual can be employed to perform Tau test and Student’s t-test,respectively.In a parallel manner,the internally Studentized local sensitivity indicator and externally Studentized local sensitivity indicator were constructed and investigated.Since the probability of not rejecting the null hypothesis when it is false(type Ⅱ error) may be too high by using Student’s t-test,and since the Tau test has a limitation in itself,both of them are not appropriate statistical tests.To circumvent this difficulty,the standard deviation involved in the standardized local sensitivity indicator can be replaced by its normalized robust least median of squares estimator,and then perform the Gaussian normal test for detection and identification of outlying observations. |
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| Keywords: | outlier sensitivity analysis Gaussian normal test Student＇s t-test Tau test |
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