The Masking Breakdown Point of Multivariate Outlier Identification Rules

Abstract

In this paper, we consider one-step outlier identication rules for multivariate data, generalizing the concept of so-called outlier identiers, as presented in Davies and Gather (1993) for the case of univariate samples. We investigate, how the nite-sample breakdown points of estimators used in these identication rules inuence the masking behaviour of the rules.

Detection of Outliers in Multivariate Data: A Method Based on Clustering and Robust Estimators

“…The identification of outliers in multivariate data is usually based on Mahalanobis distance. The use of robust estimates of the mean and the covariance matrix is advised in order to avoid the masking effect (Rousseeuw and Leroy, 1985;Rousseeuw and von Zomeren, 1990;Rocke and Woodruff, 1996;Becker and Gather, 1999). However, the performance of these rules is still highly dependent of multivariate normality of the bulk of the data.…”

Identification of Multivariate Outliers: A Performance Study

“…The other method is that of Becker and Gather (1999) which works somewhat different: A so-called α outlier with respect to N p (µ, Σ) is an element of the set…”

“…Barnett and Lewis, 1994;Rocke and Woodruff, 1996;Becker and Gather, 1999;Peña and Prieto, 2001) and different other robust estimators for multivariate location and scatter can be considered (e.g. Maronna, 1976;Davies, 1987;Tyler, 1991;Maronna and Yohai, 1995;Kent and Tyler, 1996).…”

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Abstract: Three methods for the identification of multivariate outliers (Rousseeuw and Van Zomeren, 1990;Becker and Gather, 1999;Filzmoser et al, 2005) are compared. They are based on the Mahalanobis distance that will be made resistant against outliers and model deviations by robust estimation of location and covariance.

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Dissolution and Isolation Robustness of Fixed Point Clusters

“…The principle to define the outliers is taken from Becker and Gather (1999). They define α-outliers as points that lie in a region with low density such that the probability of the so-called outlier region is α under the reference distribution.…”