Controlling the size of multivariate outlier tests with the MCD estimator of scatter |
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Authors: | Andrea Cerioli Marco Riani Anthony C Atkinson |
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Institution: | (1) Dipartimento di Economia, Università di Parma, Via Kennedy 6, 43100 Parma, Italy;(2) Department of Statistics, The London School of Economics, Houghton Street, London, WC2A 2AE, UK |
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Abstract: | 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. |
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Keywords: | Minimum covariance determinant estimator Robust distances Multiple outliers Simultaneous testing Calibration factor Simulation |
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