IDEAS home Printed from https://ideas.repec.org/a/bla/jorssb/v71y2009i2p447-466.html
   My bibliography  Save this article

Finding an unknown number of multivariate outliers

Author

Listed:
  • Marco Riani
  • Anthony C. Atkinson
  • Andrea Cerioli

Abstract

Summary. 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

  • 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.
    • Handle: RePEc:bla:jorssb:v:71:y:2009:i:2:p:447-466
    DOI: 10.1111/j.1467-9868.2008.00692.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9868.2008.00692.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1467-9868.2008.00692.x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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, vol. 126(C), pages 167-183.
    2. Pokojovy, Michael & Jobe, J. Marcus, 2022. "A robust deterministic affine-equivariant algorithm for multivariate location and scatter," Computational Statistics & Data Analysis, Elsevier, vol. 172(C).
    3. 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.
    4. Andrea Cerioli & Marco Riani & Anthony C. Atkinson & Aldo Corbellini, 2018. "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 559-587, December.
    5. Luis García-Escudero & Alfonso Gordaliza & Carlos Matrán & Agustín Mayo-Iscar, 2010. "A review of robust clustering methods," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 4(2), pages 89-109, September.
    6. J. L. Alfaro & J. Fco. Ortega, 2009. "A comparison of robust alternatives to Hotelling's T2 control chart," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(12), pages 1385-1396.
    7. Steffen Liebscher & Thomas Kirschstein, 2015. "Efficiency of the pMST and RDELA location and scatter estimators," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(1), pages 63-82, January.
    8. Cheng, Tsung-Chi, 2012. "On simultaneously identifying outliers and heteroscedasticity without specific form," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2258-2272.
    9. Pison, Greet & Rousseeuw, Peter J. & Filzmoser, Peter & Croux, Christophe, 2003. "Robust factor analysis," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 145-172, January.
    10. Gervini, Daniel, 2003. "A robust and efficient adaptive reweighted estimator of multivariate location and scatter," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 116-144, January.
    11. Sharifah Soaad Syed Yahaya & Hazlina Ali & Zurni Omar, 2011. "An Alternative Hotelling T^2 Control Chart Based on Minimum Vector Variance (MVV)," Modern Applied Science, Canadian Center of Science and Education, vol. 5(4), pages 132-132, August.
    12. Zhou, Jianhui, 2009. "Robust dimension reduction based on canonical correlation," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 195-209, January.
    13. Yunlu Jiang & Canhong Wen & Xueqin Wang, 2018. "Adaptive Exponential Power Depth with Application to Classification," Journal of Classification, Springer;The Classification Society, vol. 35(3), pages 466-480, October.
    14. Zhu, Yongmeng & Wu, Jiechang & Wu, Jun & Liu, Shuyong, 2022. "Dimensionality reduce-based for remaining useful life prediction of machining tools with multisensor fusion," Reliability Engineering and System Safety, Elsevier, vol. 218(PB).
    15. Atozou, Baoubadi & Tamini, Lota D. & Bergeronm, Stephane & Doyon, Maurice, 2020. "Factors Explaining the Hypothetical Bias: How to Improve Models for Meta-Analyses," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 45(2), March.
    16. repec:cte:wsrepe:ws1450804 is not listed on IDEAS
    17. Marco Riani & Andrea Cerioli & Francesca Torti, 2014. "On consistency factors and efficiency of robust S-estimators," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 356-387, June.
    18. Taskinen, Sara & Croux, Christophe & Kankainen, Annaliisa & Ollila, Esa & Oja, Hannu, 2006. "Influence functions and efficiencies of the canonical correlation and vector estimates based on scatter and shape matrices," Journal of Multivariate Analysis, Elsevier, vol. 97(2), pages 359-384, February.
    19. Christophe Biernacki & Alexandre Lourme, 2019. "Unifying data units and models in (co-)clustering," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(1), pages 7-31, March.
    20. Sung-Soo Kim & Sung Park & W. J. Krzanowski, 2008. "Simultaneous variable selection and outlier identification in linear regression using the mean-shift outlier model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(3), pages 283-291.
    21. Fekri, M. & Ruiz-Gazen, A., 2004. "Robust weighted orthogonal regression in the errors-in-variables model," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 89-108, January.

    More about this item

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:jorssb:v:71:y:2009:i:2:p:447-466. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/rssssea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.