The stalactite plot for the detection of multivariate outliers

Atkinson, Anthony C.; Mulira, Ham-Mukasa

doi:10.1007/bf00146951

Cited by 72 publications

(42 citation statements)

References 5 publications

(5 reference statements)

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“…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.…”

Section: Example 1: Stack Loss Datamentioning

confidence: 99%

“…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.…”

Section: Example 1: Stack Loss Datamentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

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Fast Very Robust Methods for the Detection of Multiple Outliers

Atkinson

1994

Journal of the American Statistical Association

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JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship.A few repeats of a simple forward search from a random starting point are shown to provide sufficiently robust parameter estimates to reveal masked multiple outliers. The stability of the patterns obtained is exhibited by the stalactite plot. The robust estimators used are least median of squares for regression and the minimum volume ellipsoid for multivariate outliers. The forward search also has potential as an algorithm for calculation of these parameter estimates. For large problems, parallel computing provides appreciable reduction in computational time.

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Section: Example 1: Stack Loss Datamentioning

confidence: 99%

Section: Example 1: Stack Loss Datamentioning

confidence: 99%

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Fast Very Robust Methods for the Detection of Multiple Outliers

Atkinson

1994

Journal of the American Statistical Association

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“…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.…”

Section: The Modified MCDmentioning

confidence: 99%

Fast Algorithms for Computing High Breakdown Covariance Matrices with Missing Data

Copt

Victoria‐Feser

2004

Theory and Applications of Recent Robust Methods

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Abstract. Robust estimation of covariance matrices when some of the data at hand are missing is an important problem. It has been studied by Little and Smith (1987) and more recently by Cheng and Victoria-Feser (2002). The latter propose the use of high breakdown estimators and so-called hybrid algorithms (see, e.g., Woodruff and Rocke, 1994). In particular, the minimum volume ellipsoid of Rousseeuw (1984) is adapted to the case of missing data. To compute it, they use (a modified version of) the forward search algorithm (see e.g. Atkinson, 1994). In this paper, we propose to use instead a modification of the C-step algorithm proposed by Rousseeuw and Van Driessen (1999) which is actually a lot faster. We also adapt the orthogonalized GnanadesikanKettenring (OGK) estimator proposed by Maronna and Zamar (2002) to the case of missing data and use it as a starting point for an adapted S-estimator. Moreover, we conduct a simulation study to compare different robust estimators in terms of their efficiency and breakdown. Mathematics Subject Classification (2000). Primary 62G35; Secondary 62H12.

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“…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.…”

Section: Introductionmentioning

confidence: 99%