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AN ADAPTIVE TRIMMED LIKELIHOOD ALGORITHM FOR IDENTIFICATION OF MULTIVARIATE OUTLIERS
Author(s) -
Clarke Brenton R.,
Schubert Daniel D.
Publication year - 2006
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/j.1467-842x.2006.00445.x
Subject(s) - mathematics , outlier , estimator , multivariate statistics , covariance , trimming , maxima and minima , statistics , measure (data warehouse) , robust statistics , data set , trimmed estimator , identification (biology) , variance (accounting) , minimum variance unbiased estimator , consistent estimator , data mining , computer science , mathematical analysis , botany , accounting , biology , business , operating system
Summary This article describes an algorithm for the identification of outliers in multivariate data based on the asymptotic theory for location estimation as described typically for the trimmed likelihood estimator and in particular for the minimum covariance determinant estimator. The strategy is to choose a subset of the data which minimizes an appropriate measure of the asymptotic variance of the multivariate location estimator. Observations not belonging to this subset are considered potential outliers which should be trimmed. For α less than about 0.5, the correct trimming proportion is taken to be that α > 0 for which the minimum of any minima of this measure of the asymptotic variance occurs. If no minima occur for an α > 0 then the data set will be considered outlier free.