Journal of the American Statistical Association · 1990 · 461 citations · 0 references
ComputingVisualizationMultivariate VisualizationSpatial Data AnalysisSpatial StatisticsMultivariate AnalysisOutlier DetectionOutlier HandlingRobust Statistical ModelingRobust StatisticsDistance-based Outlier DetectionLeverage PointsMaskingMultivariate Outlier DetectionOutlier IdentificationPoint Outlier DetectionRobust EstimationRobust Regression
Detecting outliers in multivariate data is challenging because classical methods based on sample mean and covariance are themselves affected by outliers, leading to masking, a problem that also occurs in regression with least squares. The authors aim to avoid masking by computing distances from robust location and covariance estimates and by introducing a display that plots robust regression residuals against these distances. They compute robust distances using robust location and covariance estimates and plot robust regression residuals versus these distances to classify observations. Robust distances and a robust regression display effectively expose and classify outliers and leverage points, as demonstrated in several examples.
Abstract Detecting outliers in a multivariate point cloud is not trivial, especially when there are several outliers. The classical identification method does not always find them, because it is based on the sample mean and covariance matrix, which are themselves affected by the outliers. That is how the outliers get masked. To avoid the masking effect, we propose to compute distances based on very robust estimates of location and covariance. These robust distances are better suited to expose the outliers. In the case of regression data, the classical least squares approach masks outliers in a similar way. Also here, the outliers may be unmasked by using a highly robust regression method. Finally, a new display is proposed in which the robust regression residuals are plotted versus the robust distances. This plot classifies the data into regular observations, vertical outliers, good leverage points, and bad leverage points. Several examples are discussed.