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Finding an unknown number of multivariate outliers

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  • Riani, Marco
  • Atkinson, Anthony C.
  • Cerioli, Andrea

Abstract

We use the forward search to provide robust Mahalanobis distances to detect the presence of outliers in a sample of multivariate normal data. Theoretical results on order statistics and on estimation in truncated samples provide the distribution of our test statistic. We also introduce several new robust distances with associated distributional results. Comparisons of our procedure with tests using other robust Mahalanobis distances show the good size and high power of our procedure. We also provide a unification of results on correction factors for estimation from truncated samples.

Suggested Citation

  • Riani, Marco & Atkinson, Anthony C. & Cerioli, Andrea, 2009. "Finding an unknown number of multivariate outliers," LSE Research Online Documents on Economics 30462, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:30462
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    References listed on IDEAS

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    1. Atkinson, A.C. & Riani, M., 2007. "Exploratory tools for clustering multivariate data," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 272-285, September.
    2. Garcia-Escudero, Luis Angel & Gordaliza, Alfonso, 2005. "Generalized Radius Processes for Elliptically Contoured Distributions," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1036-1045, September.
    3. Croux, Christophe & Haesbroeck, Gentiane, 1999. "Influence Function and Efficiency of the Minimum Covariance Determinant Scatter Matrix Estimator," Journal of Multivariate Analysis, Elsevier, vol. 71(2), pages 161-190, November.
    4. U. Gather & J. Pawlitschko & I. Pigeot, 1997. "A note on invariance of multiple tests," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 51(3), pages 366-372, November.
    5. Wisnowski, James W. & Montgomery, Douglas C. & Simpson, James R., 2001. "A Comparative analysis of multiple outlier detection procedures in the linear regression model," Computational Statistics & Data Analysis, Elsevier, vol. 36(3), pages 351-382, May.
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    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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