引用本文: 王海涛, 欧吉坤, 袁运斌, 郭建锋. 估计观测值粗差三种方法的等价性讨论[J]. 武汉大学学报 ( 信息科学版), 2013, 38(2): 162-166.
WANG Haitao, OU Jikun, YUAN Yunbin, GUO Jianfeng. On Equivalence of Three Estimators for Outliers in Linear Mode[J]. Geomatics and Information Science of Wuhan University, 2013, 38(2): 162-166.
 Citation: WANG Haitao, OU Jikun, YUAN Yunbin, GUO Jianfeng. On Equivalence of Three Estimators for Outliers in Linear Mode[J]. Geomatics and Information Science of Wuhan University, 2013, 38(2): 162-166.

## On Equivalence of Three Estimators for Outliers in Linear Mode

• 摘要: 在粗差定位一致的前提下,证明了拟准检定法与部分最小二乘法的粗差估值具有等价性;LEGE法粗差估值与部分最小二乘法粗差估值具有等价性,其条件为未受污染观测值等权独立,且与受污染观测值相互独立。仿真算例证明,当未受粗差污染观测值不等权时,拟准检定法与部分最小二乘法得到的粗差估值结果相同,均比LEGE法粗差估值结果更准确、精度更高。

Abstract: Detecting and manipulating multiple outliers is one of the most challenging topics in the research area of observation data quality control.There are four popular methods dealing with this issue,including data snooping,the method of simultaneous locating and evaluating multidimensional gross errors(LEGE),quasi-accurate detection of gross errors(QUAD),and part least squares(PLS).The outlier estimation formulas of the four methods appear much different.It has been justified that the outlier estimations of data snooping and LEGE are equivalent under certain condition.Thus the efforts of this presentation are focused on discussing the outlier estimation equivalence of the last three methods.The preliminary assumption of the discussion is that the outliers have been successfully located.We have two conclusions.First,the outlier estimation of QUAD is equivalent to that of PLS.Second,the outlier estimation of LEGE equals that of PLS under the condition when the clean observation data(the first data group) has equal weights and is independent of the contaminated observation data(the second data group).The simulated testing example reveals that if the clean data are not equally weighted,the outlier estimation of QUAD is equal to that of PLS,but both are more accurate and precise than the outlier estimation of LEGE.

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