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Multivariate outliers

Rodrigues, Isabel M.; Boente, Graciela

International Encyclopedia of Statistical Science, Springer-Verlag, Berlin Heidelberg, (2011), 910-912

In the statistical analysis of data one is often confronted with observations that “appear to be inconsistent with the remainder of that set of data” (Barnett and Lewis 1994). Although such observations (the outliers) have been the subject of numerous investigations, there is no general accepted formal definition of outlyingness. Nevertheless, the outliers describe abnormal data behavior, i.e., data that are deviating from the natural data variability (see, e.g., Peña and Prieto 2001, Filzmoser 2004, and Filzmoser et al. 2008 for a discussion).

Sometimes outliers can grossly distort the statistical analysis, while at other times their influence may not be as noticeable. Statisticians have accordingly developed numerous algorithms for the detection and treatment of outliers, but most of these methods were developed for univariate data sets. They are based on the estimation of location and scale, or on quantiles of the data. Since in a univariate sample outliers may be identified as an ex ...