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Identification of local multivariate outliers

Author

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  • Peter Filzmoser
  • Anne Ruiz-Gazen
  • Christine Thomas-Agnan

Abstract

The Mahalanobis distance between pairs of multivariate observations is used as a measure of similarity between the observations. The theoretical distribution is derived, and the result is used for judging on the degree of isolation of an observation. In case of spatially dependent data where spatial coordinates are available, different exploratory tools are introduced for studying the degree of isolation of an observation from a fraction of its neighbors, and thus to identify local multivariate outliers. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Peter Filzmoser & Anne Ruiz-Gazen & Christine Thomas-Agnan, 2014. "Identification of local multivariate outliers," Statistical Papers, Springer, vol. 55(1), pages 29-47, February.
    • Handle: RePEc:spr:stpapr:v:55:y:2014:i:1:p:29-47
    DOI: 10.1007/s00362-013-0524-z
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    References listed on IDEAS

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    1. Cerioli, Andrea & Farcomeni, Alessio & Riani, Marco, 2013. "Robust distances for outlier-free goodness-of-fit testing," Computational Statistics & Data Analysis, Elsevier, vol. 65(C), pages 29-45.
    2. Marco Riani & Anthony C. Atkinson & Andrea Cerioli, 2009. "Finding an unknown number of multivariate outliers," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 447-466, April.
    3. Cerioli, Andrea, 2010. "Multivariate Outlier Detection With High-Breakdown Estimators," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 147-156.
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    Cited by:

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    2. Brenton R. Clarke & Andrew Grose, 2023. "A further study comparing forward search multivariate outlier methods including ATLA with an application to clustering," Statistical Papers, Springer, vol. 64(2), pages 395-420, April.
    3. Andrea Cerioli & Marco Riani & Anthony C. Atkinson & Aldo Corbellini, 2018. "Rejoinder to the discussion of “The power of monitoring: how to make the most of a contaminated multivariate sample”," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(4), pages 661-666, December.
    4. Fernanda De Bastiani & Audrey Mariz de Aquino Cysneiros & Miguel Uribe-Opazo & Manuel Galea, 2015. "Influence diagnostics in elliptical spatial linear models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 322-340, June.
    5. Tarr, G. & Müller, S. & Weber, N.C., 2016. "Robust estimation of precision matrices under cellwise contamination," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 404-420.

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