IDEAS home Printed from https://ideas.repec.org/a/taf/jnlasa/v107y2012i499p1178-1186.html
   My bibliography  Save this article

Robust Estimation of Multivariate Location and Scatter in the Presence of Missing Data

Author

Listed:
  • Mike Danilov
  • Víctor J. Yohai
  • Ruben H. Zamar

Abstract

Two main issues regarding data quality are data contamination (outliers) and data completion (missing data). These two problems have attracted much attention and research but surprisingly, they are seldom considered together. Popular robust methods such as S -estimators of multivariate location and scatter offer protection against outliers but cannot deal with missing data, except for the obviously inefficient approach of deleting all incomplete cases. We generalize the definition of S -estimators of multivariate location and scatter to simultaneously deal with missing data and outliers. We show that the proposed estimators are strongly consistent under elliptical models when data are missing completely at random . We derive an algorithm similar to the Expectation-Maximization algorithm for computing the proposed estimators. This algorithm is initialized by an extension for missing data of the minimum volume ellipsoid. We assess the performance of our proposal by Monte Carlo simulation and give some real data examples. This article has supplementary material online.

Suggested Citation

  • Mike Danilov & Víctor J. Yohai & Ruben H. Zamar, 2012. "Robust Estimation of Multivariate Location and Scatter in the Presence of Missing Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 1178-1186, September.
    • Handle: RePEc:taf:jnlasa:v:107:y:2012:i:499:p:1178-1186
    DOI: 10.1080/01621459.2012.699792
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/01621459.2012.699792
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/01621459.2012.699792?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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Nikola Štefelová & Andreas Alfons & Javier Palarea-Albaladejo & Peter Filzmoser & Karel Hron, 2021. "Robust regression with compositional covariates including cellwise outliers," 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. 15(4), pages 869-909, December.
    2. Stefan Van Aelst, 2015. "Comments on: Robust estimation of multivariate location and scatter in the presence of cellwise and casewise contamination," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 478-481, September.
    3. Leung, Andy & Yohai, Victor & Zamar, Ruben, 2017. "Multivariate location and scatter matrix estimation under cellwise and casewise contamination," Computational Statistics & Data Analysis, Elsevier, vol. 111(C), pages 59-76.
    4. Claudio Agostinelli & Andy Leung & Victor Yohai & Ruben Zamar, 2015. "Robust estimation of multivariate location and scatter in the presence of cellwise and casewise contamination," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 441-461, September.
    5. Leung, Andy & Zhang, Hongyang & Zamar, Ruben, 2016. "Robust regression estimation and inference in the presence of cellwise and casewise contamination," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 1-11.
    6. Giovanni Saraceno & Claudio Agostinelli, 2021. "Robust multivariate estimation based on statistical depth filters," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(4), pages 935-959, December.
    7. Claudio Agostinelli & Andy Leung & Victor Yohai & Ruben Zamar, 2015. "Rejoinder on: Robust estimation of multivariate location and scatter in the presence of cellwise and casewise contamination," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 484-488, September.
    8. Stephane Heritier & Maria-Pia Victoria-Feser, 2018. "Discussion of “The power of monitoring: how to make the most of a contaminated multivariate sample” by Andrea Cerioli, Marco Riani, Anthony C. Atkinson and Aldo Corbellini," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(4), pages 595-602, December.
    9. Henry Velasco & Henry Laniado & Mauricio Toro & Víctor Leiva & Yuhlong Lio, 2020. "Robust Three-Step Regression Based on Comedian and Its Performance in Cell-Wise and Case-Wise Outliers," Mathematics, MDPI, vol. 8(8), pages 1-18, August.
    10. Lafit, Ginette & Nogales Martín, Francisco Javier, 2017. "Robust and sparse estimation of high-dimensional precision matrices via bivariate outlier detection," DES - Working Papers. Statistics and Econometrics. WS 24534, Universidad Carlos III de Madrid. Departamento de Estadística.
    11. Christophe Croux & Viktoria Öllerer, 2015. "Comments on: Robust estimation of multivariate location and scatter in the presence of cellwise and casewise contamination," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 462-466, September.
    12. Frahm, Gabriel & Nordhausen, Klaus & Oja, Hannu, 2020. "M-estimation with incomplete and dependent multivariate data," Journal of Multivariate Analysis, Elsevier, vol. 176(C).

    More about this item

    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:taf:jnlasa:v:107:y:2012:i:499:p:1178-1186. 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.

    We have no bibliographic references for this item. You can help adding them by using 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/UASA20 .

    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.