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Finding an unknown number of multivariate outliers

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  • Marco Riani
  • Anthony C. Atkinson
  • Andrea Cerioli
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    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. Copyright (c) 2009 Royal Statistical Society.

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    Bibliographic Info

    Article provided by Royal Statistical Society in its journal Journal of the Royal Statistical Society: Series B (Statistical Methodology).

    Volume (Year): 71 (2009)
    Issue (Month): 2 ()
    Pages: 447-466

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    Handle: RePEc:bla:jorssb:v:71:y:2009:i:2:p:447-466

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    Cited by:
    1. Kirschstein, Thomas & Liebscher, Steffen & Becker, Claudia, 2013. "Robust estimation of location and scatter by pruning the minimum spanning tree," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 120(C), pages 173-184.
    2. Jan Kalina, 2012. "On Multivariate Methods in Robust Econometrics," Prague Economic Papers, University of Economics, Prague, University of Economics, Prague, vol. 2012(1), pages 69-82.
    3. Salvatore Ingrassia & Simona Minotti & Giorgio Vittadini, 2012. "Local Statistical Modeling via a Cluster-Weighted Approach with Elliptical Distributions," Journal of Classification, Springer, Springer, vol. 29(3), pages 363-401, October.
    4. Menjoge, Rajiv S. & Welsch, Roy E., 2010. "A diagnostic method for simultaneous feature selection and outlier identification in linear regression," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 54(12), pages 3181-3193, December.
    5. Søren Johansen & Bent Nielsen, 2013. "Asymptotic analysis of the Forward Search," Discussion Papers 13-01, University of Copenhagen. Department of Economics.
    6. Domenico Perrotta & Marco Riani & Francesca Torti, 2009. "New robust dynamic plots for regression mixture detection," Advances in Data Analysis and Classification, Springer, Springer, vol. 3(3), pages 263-279, December.
    7. Cerioli, Andrea & Farcomeni, Alessio & Riani, Marco, 2014. "Strong consistency and robustness of the Forward Search estimator of multivariate location and scatter," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 126(C), pages 167-183.
    8. Riani, Marco & Atkinson, Anthony C., 2010. "Robust model selection with flexible trimming," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 54(12), pages 3300-3312, December.
    9. Bellini, Tiziano & Riani, Marco, 2012. "Robust analysis of default intensity," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 56(11), pages 3276-3285.
    10. Tiziano Bellini, 2010. "Detecting atypical observations in financial data: the forward search for elliptical copulas," Advances in Data Analysis and Classification, Springer, Springer, vol. 4(4), pages 287-299, December.
    11. Cerioli, Andrea & Farcomeni, Alessio, 2011. "Error rates for multivariate outlier detection," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 55(1), pages 544-553, January.
    12. Valentin Todorov & Matthias Templ & Peter Filzmoser, 2011. "Detection of multivariate outliers in business survey data with incomplete information," Advances in Data Analysis and Classification, Springer, Springer, vol. 5(1), pages 37-56, April.
    13. Luigi Grossi & Fabrizio Laurini, 2011. "Robust estimation of efficient mean–variance frontiers," Advances in Data Analysis and Classification, Springer, Springer, vol. 5(1), pages 3-22, April.
    14. Cerioli, Andrea & Farcomeni, Alessio & Riani, Marco, 2013. "Robust distances for outlier-free goodness-of-fit testing," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 65(C), pages 29-45.

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