IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v34y2007i10p1241-1250.html
   My bibliography  Save this article

Robust Detection of Multiple Outliers in Grouped Multivariate Data

Author

Listed:
  • Chrys Caroni
  • Nedret Billor

Abstract

Many methods have been developed for detecting multiple outliers in a single multivariate sample, but very few for the case where there may be groups in the data. We propose a method of simultaneously determining groups (as in cluster analysis) and detecting outliers, which are points that are distant from every group. Our method is an adaptation of the BACON algorithm proposed by Billor, Hadi and Velleman for the robust detection of multiple outliers in a single group of multivariate data. There are two versions of our method, depending on whether or not the groups can be assumed to have equal covariance matrices. The effectiveness of the method is illustrated by its application to two real data sets and further shown by a simulation study for different sample sizes and dimensions for 2 and 3 groups, with and without planted outliers in the data. When the number of groups is not known in advance, the algorithm could be used as a robust method of cluster analysis, by running it for various numbers of groups and choosing the best solution.

Suggested Citation

  • Chrys Caroni & Nedret Billor, 2007. "Robust Detection of Multiple Outliers in Grouped Multivariate Data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(10), pages 1241-1250.
    • Handle: RePEc:taf:japsta:v:34:y:2007:i:10:p:1241-1250
    DOI: 10.1080/02664760701592877
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/02664760701592877
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/02664760701592877?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. N. A. Campbell, 1980. "Robust Procedures in Multivariate Analysis I: Robust Covariance Estimation," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 29(3), pages 231-237, November.
    2. Billor, Nedret & Hadi, Ali S. & Velleman, Paul F., 2000. "BACON: blocked adaptive computationally efficient outlier nominators," Computational Statistics & Data Analysis, Elsevier, vol. 34(3), pages 279-298, September.
    3. M. J. Baxter, 1995. "Standardization and Transformation in Principal Component Analysis, with Applications to Archaeometry," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 44(4), pages 513-527, December.
    4. Hardin, Johanna & Rocke, David M., 2004. "Outlier detection in the multiple cluster setting using the minimum covariance determinant estimator," Computational Statistics & Data Analysis, Elsevier, vol. 44(4), pages 625-638, January.
    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. Catherine Fuss & Angelos Theodorakopoulos, 2018. "Compositional Changes in Aggregate Productivity in an Era of Globalisation and Financial Crisis," Working Papers of VIVES - Research Centre for Regional Economics 627696, KU Leuven, Faculty of Economics and Business (FEB), VIVES - Research Centre for Regional Economics.
    2. L. Pitsoulis & G. Zioutas, 2010. "A fast algorithm for robust regression with penalised trimmed squares," Computational Statistics, Springer, vol. 25(4), pages 663-689, December.
    3. Cristian BARRA & Roberto ZOTTI, 2019. "Bank Performance, Financial Stability And Market Concentration: Evidence From Cooperative And Non‐Cooperative Banks," Annals of Public and Cooperative Economics, Wiley Blackwell, vol. 90(1), pages 103-139, March.
    4. Leopold Simar & Paul Wilson, 2000. "A general methodology for bootstrapping in non-parametric frontier models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(6), pages 779-802.
    5. Hong Choon Ong & Ekele Alih, 2015. "A Control Chart Based on Cluster-Regression Adjustment for Retrospective Monitoring of Individual Characteristics," PLOS ONE, Public Library of Science, vol. 10(4), pages 1-30, April.
    6. Michael S. Delgado & Daniel J. Henderson & Christopher F. Parmeter, 2014. "Does Education Matter for Economic Growth?," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 76(3), pages 334-359, June.
    7. Stefani, Gianluca & Gadanakis, Yiorgos & Lombardi, Ginevra Virginia & Tiberti, Marco, 2017. "The impact of financial leverage on farms capacity to react in market shocks," 2017 International Congress, August 28-September 1, 2017, Parma, Italy 261156, European Association of Agricultural Economists.
    8. Peter Nemec, 2024. "Contesting the public works domain: examining the factors affecting presence and success of SMES in public procurement," Empirical Economics, Springer, vol. 67(5), pages 2135-2173, November.
    9. Batalla-Bejerano, Joan & Costa-Campi, Maria Teresa & Trujillo-Baute, Elisa, 2016. "Collateral effects of liberalisation: Metering, losses, load profiles and cost settlement in Spain’s electricity system," Energy Policy, Elsevier, vol. 94(C), pages 421-431.
    10. A.A.M. Nurunnabi & M. Nasser & A.H.M.R. Imon, 2016. "Identification and classification of multiple outliers, high leverage points and influential observations in linear regression," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(3), pages 509-525, March.
    11. Wessel N. van Wieringen & Carel F. W. Peeters & Renee X. de Menezes & Mark A. van de Wiel, 2018. "Testing for pathway (in)activation by using Gaussian graphical models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 67(5), pages 1419-1436, November.
    12. Essid, Hédi & Ouellette, Pierre & Vigeant, Stéphane, 2010. "Measuring efficiency of Tunisian schools in the presence of quasi-fixed inputs: A bootstrap data envelopment analysis approach," Economics of Education Review, Elsevier, vol. 29(4), pages 589-596, August.
    13. Jiří Schwarz & Martin Pospíšil, 2018. "Bankruptcy, Investment, and Financial Constraints: Evidence from the Czech Republic," Eastern European Economics, Taylor & Francis Journals, vol. 56(2), pages 99-121, March.
    14. AMENDOLA, Adalgiso & BARRA, Cristian & BOCCIA, Marinella & PAPACCIO, Anna, 2018. "Market Structure and Financial Stability: Theory and Evidence," CELPE Discussion Papers 156, CELPE - CEnter for Labor and Political Economics, University of Salerno, Italy.
    15. Bedri Kamil Onur Tas, 2024. "A machine learning approach to detect collusion in public procurement with limited information," Journal of Computational Social Science, Springer, vol. 7(2), pages 1913-1935, October.
    16. Alper Sinan & B. Barıs Alkan, 2015. "A useful approach to identify the multicollinearity in the presence of outliers," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(5), pages 986-993, May.
    17. Fratianni, Michele & Marchionne, Francesco, 2017. "Bank asset reallocation and sovereign debt," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 47(C), pages 15-32.
    18. Janz, Norbert, 1997. "Robust GMM Estimation of an Euler Equation Investment Model with German Firm Level Panel Data," ZEW Discussion Papers 97-05, ZEW - Leibniz Centre for European Economic Research.
    19. José Ignacio Giménez-Nadal & José Alberto Molina & Jorge Velilla, 2024. "Intermediate activities while commuting," Review of Economics of the Household, Springer, vol. 22(3), pages 1185-1220, September.
    20. Sylvain Weber, 2010. "bacon: An effective way to detect outliers in multivariate data using Stata (and Mata)," Stata Journal, StataCorp LP, vol. 10(3), pages 331-338, September.

    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:taf:japsta:v:34:y:2007:i:10:p:1241-1250. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/CJAS20 .

    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.