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What is the relation between smearing effect of least squares estimation and its influence function?
Survey Review ( IF 1.2 ) Pub Date : 2021-06-17 , DOI: 10.1080/00396265.2021.1939590
Utkan Mustafa Durdag 1 , Serif Hekimoglu 2 , Bahattin Erdogan 2
Affiliation  

In some cases, tests for outliers and robust methods based on the Least Square Estimation (LSE) fail to detect and isolate outliers. LSE 'smears the effect' of an outlier on all estimates of the residuals, the unknowns, and the a posteriori variance of unit weight. Therefore as bias goes to infinity, the Influence Function (IF) also goes to infinity. This study aims to investigate the effect of an outlier on the unknown parameters, etc., compared to the IF concept. Moreover, how the ratio of the resulting outlier effect is related to the redundancy of the geodetic network has been shown through the concepts of Sensitivity Curve (SC) and smearing effect by Monte Carlo Simulation. Also, it has proved that the SC of LSE was almost equal to the ‘smearing effect’ of LSE, which behaves systematically as a function of the partial redundancy that varies from one residual to another in the geodetic network.



中文翻译:

最小二乘估计的拖尾效应与其影响函数有什么关系?

在某些情况下,异常值测试和基于最小二乘估计 (LSE) 的稳健方法无法检测和隔离异常值。LSE 对残差、未知数和单位权重的后验方差的所有估计值“涂抹”异常值的影响。因此,随着偏差趋于无穷大,影响函数 (IF) 也趋于无穷大。本研究旨在研究与 IF 概念相比,异常值对未知参数等的影响。此外,通过蒙特卡洛模拟的灵敏度曲线(SC)和拖尾效应的概念,已经显示了由此产生的异常值效应的比率与大地测量网络的冗余度之间的关系。此外,已经证明 LSE 的 SC 几乎等于 LSE 的“拖尾效应”,

更新日期:2021-06-17
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