Identifying Multiple Outliers in Multivariate Data

Abstract

SUMMARY We propose a procedure for the detection of multiple outliers in multivariate data. Let X be an n × p data matrix representing n observations on p variates. We first order the n observations, using an appropriately chosen robust measure of outlyingness, then divide the data set into two initial subsets: A ‘basic’ subset which contains p +1 ‘good’ observations and a ‘non‐basic’ subset which contains the remaining n ‐ p ‐ 1 observations. Second, we compute the relative distance from each point in the data set to the centre of the basic subset, relative to the (possibly singular) covariance matrix of the basic subset. Third, we rearrange the n observations in ascending order accordingly, then divide the data set into two subsets: A basic subset which contains the first p + 2 observations and a non‐basic subset which contains the remaining n ‐ p ‐ 2 observations. This process is repeated until an appropriately chosen stopping criterion is met. The final non‐basic subset of observations is declared an outlying subset. The procedure proposed is illustrated and compared with existing methods by using several data sets. The procedure is simple, computationally inexpensive, suitable for automation, computable with widely available software packages, effective in dealing with masking and swamping problems and, most importantly, successful in identifying multivariate outliers.

How does the age structure of worker flows affect firm performance?

“…This indicates that the linking of the individual and firm data is incomplete. Second, we remove some potentially influential outliers that we detected by using the method proposed by Hadi (1992Hadi ( , 1994. The method is useful for finding multiple outliers in multivariate data.…”

The curse of aid

“…32 Finally, we consider the effect of eliminating the outliers on the results of the estimation. Following Roodman (2007) and Easterly et al (2004), outliers are chosen by applying the Hadi (1992) procedure, using 0.05 as the cut-off significant level. Table 12 presents the results of different estimation procedure in the cross section sample once the outliers are eliminated.…”

The stalactite plot for the detection of multivariate outliers

“…Outliers will only be included as m approaches n, when no good observations remain to be introduced into the fit. Hadi (1992) uses the same forward algorithm starting from robust estimates of the means and covariances for calculation of the initial Mahalanobis distances. His forward search terminates when m is the median of the number of observations when allowance is made for the effect of fitting.…”