The stalactite plot for the detection of multivariate outliers

Abstract

Detection of multiple outliers in multivariate data using Mahalanobis distances requires robust estimates of the means and covariance of the data. We obtain this by sequential construction of an outlier free subset of the data, starting from a small random subset. The stalactite plot provides a cogent summary of suspected outliers as the subset size increases. The dependence on subset size can be virtually removed by a simulation-based normalization. Combined with probability plots and resampling procedures, the stalactite plot, particularly in its normalized form, leads to identification of multivariate outliers, even in the presence of appreciable masking.

Fast Very Robust Methods for the Detection of Multiple Outliers

“…If a first-order model in the three explanatory variables is fitted, it is standard that observations 1, 3, 4, and 21 are outliers. LMS analyses of the data have been given by Atkinson (1986), Hampel, Ronchetti, Rousseeuw, and Stahel (1986, p. 332), and Rousseeuw and Leroy (1987, p. 78). 267-268) gave a brief history of analyses.…”

“…Figure la is the stalactite plot for one of the two best solutions found, for both of which & = .896, compared with 1.0 for the best solution found by Atkinson (1986) from searching over elemental sets. Figure la is the stalactite plot for one of the two best solutions found, for both of which & = .896, compared with 1.0 for the best solution found by Atkinson (1986) from searching over elemental sets.…”

“…The pattern of multivariate outliers found during each search can be exhibited using the stalactite plot of Atkinson and Mulira (1993). Atkinson (1993) described the fast forward algorithm for multivariate outliers.…”

Fast Algorithms for Computing High Breakdown Covariance Matrices with Missing Data

“…To run the M CD, Cheng and Victoria-Feser (2002) adapt the forward search algorithm proposed by Atkinson (1993Atkinson ( , 1994. However, more recently Rousseeuw and Van Driessen (1999) have proposed a new algorithm called FAST-MCD supposed to be even faster than the forward search algorithm and able to deal with very large data sets.…”

The Masking Breakdown Point of Multivariate Outlier Identification Rules

“…Some methods proposed for the identication of outliers in multivariate samples are of heuristic nature (e.g. Atkinson and Mulira, 1993, Bacon-Shone and Fung, 1987, Barnett and Lewis, 1994, p. 307 ., Bhandary, 1992, others are of consecutive testing type (see Barnett and Lewis, 1994, chap. 7.3, Caroni and Prescott, 1992, Hara, 1988, Hawkins, 1980, chap.…”