On Equivalence of Three Estimators for Outliers in Linear Mode

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.