An Adaptive Trimmed Likelihood Algorithm for Identification of Multivariate Outliers

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.