Statistics and Computing

, 19:341 | Cite as

Controlling the size of multivariate outlier tests with the MCD estimator of scatter

  • Andrea CerioliEmail author
  • Marco Riani
  • Anthony C. Atkinson


Multivariate outlier detection requires computation of robust distances to be compared with appropriate cut-off points. In this paper we propose a new calibration method for obtaining reliable cut-off points of distances derived from the MCD estimator of scatter. These cut-off points are based on a more accurate estimate of the extreme tail of the distribution of robust distances. We show that our procedure gives reliable tests of outlyingness in almost all situations of practical interest, provided that the sample size is not much smaller than 50. Therefore, it is a considerable improvement over all the available MCD procedures, which are unable to provide good control over the size of multiple outlier tests for the data structures considered in this paper.


Minimum covariance determinant estimator Robust distances Multiple outliers Simultaneous testing Calibration factor Simulation 


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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Andrea Cerioli
    • 1
    Email author
  • Marco Riani
    • 1
  • Anthony C. Atkinson
    • 2
  1. 1.Dipartimento di EconomiaUniversità di ParmaParmaItaly
  2. 2.Department of StatisticsThe London School of EconomicsLondonUK

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