IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v135y2015icp89-105.html
   My bibliography  Save this article

Spatial sign correlation

Author

Listed:
  • Dürre, Alexander
  • Vogel, Daniel
  • Fried, Roland

Abstract

A robust correlation estimator based on the spatial sign covariance matrix (SSCM) is proposed. We derive its asymptotic distribution and influence function at elliptical distributions. Finite sample and robustness properties are studied and compared to other robust correlation estimators by means of numerical simulations.

Suggested Citation

  • Dürre, Alexander & Vogel, Daniel & Fried, Roland, 2015. "Spatial sign correlation," Journal of Multivariate Analysis, Elsevier, vol. 135(C), pages 89-105.
    • Handle: RePEc:eee:jmvana:v:135:y:2015:i:c:p:89-105
    DOI: 10.1016/j.jmva.2014.12.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X1400267X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2014.12.002?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. Taskinen, Sara & Kankainen, Annaliisa & Oja, Hannu, 2003. "Sign test of independence between two random vectors," Statistics & Probability Letters, Elsevier, vol. 62(1), pages 9-21, March.
    2. Tyler, David E., 2010. "A note on multivariate location and scatter statistics for sparse data sets," Statistics & Probability Letters, Elsevier, vol. 80(17-18), pages 1409-1413, September.
    3. N. Locantore & J. Marron & D. Simpson & N. Tripoli & J. Zhang & K. Cohen & Graciela Boente & Ricardo Fraiman & Babette Brumback & Christophe Croux & Jianqing Fan & Alois Kneip & John Marden & Daniel P, 1999. "Robust principal component analysis for functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 8(1), pages 1-73, June.
    4. Daniel Gervini, 2008. "Robust functional estimation using the median and spherical principal components," Biometrika, Biometrika Trust, vol. 95(3), pages 587-600.
    5. Nordhausen, Klaus & Oja, Hannu, 2011. "Multivariate L1 Statistical Methods: The Package MNM," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 43(i05).
    6. Dürre, Alexander & Vogel, Daniel & Tyler, David E., 2014. "The spatial sign covariance matrix with unknown location," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 107-117.
    7. Christophe Croux & Catherine Dehon, 2010. "Influence functions of the Spearman and Kendall correlation measures," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(4), pages 497-515, November.
    8. Ma, Yanyuan & Genton, Marc G., 2001. "Highly Robust Estimation of Dispersion Matrices," Journal of Multivariate Analysis, Elsevier, vol. 78(1), pages 11-36, July.
    9. C. Croux & C. Dehon & A. Yadine, 2010. "The k-step spatial sign covariance matrix," 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 137-150, September.
    10. Marden, John I., 1999. "Some robust estimates of principal components," Statistics & Probability Letters, Elsevier, vol. 43(4), pages 349-359, July.
    11. Paindaveine, Davy, 2008. "A canonical definition of shape," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2240-2247, October.
    12. Genton, Marc G. & Ma, Yanyuan, 1999. "Robustness properties of dispersion estimators," Statistics & Probability Letters, Elsevier, vol. 44(4), pages 343-350, October.
    13. 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.
    14. 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.
    15. Todorov, Valentin & Filzmoser, Peter, 2009. "An Object-Oriented Framework for Robust Multivariate Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 32(i03).
    16. Seija Sirkiä & Sara Taskinen & Hannu Oja & David Tyler, 2009. "Tests and estimates of shape based on spatial signs and ranks," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(2), pages 155-176.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Dürre, Alexander & Tyler, David E. & Vogel, Daniel, 2016. "On the eigenvalues of the spatial sign covariance matrix in more than two dimensions," Statistics & Probability Letters, Elsevier, vol. 111(C), pages 80-85.
    2. Davy Paindaveine & Julien Remy & Thomas Verdebout, 2019. "Sign Tests for Weak Principal Directions," Working Papers ECARES 2019-01, ULB -- Universite Libre de Bruxelles.
    3. Xu, Yangchang & Xia, Ningning, 2023. "On the eigenvectors of large-dimensional sample spatial sign covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 193(C).
    4. Raymaekers, Jakob & Rousseeuw, Peter, 2019. "A generalized spatial sign covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 94-111.
    5. Dürre, Alexander & Vogel, Daniel, 2016. "Asymptotics of the two-stage spatial sign correlation," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 54-67.

    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. Taskinen, Sara & Koch, Inge & Oja, Hannu, 2012. "Robustifying principal component analysis with spatial sign vectors," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 765-774.
    2. Dürre, Alexander & Tyler, David E. & Vogel, Daniel, 2016. "On the eigenvalues of the spatial sign covariance matrix in more than two dimensions," Statistics & Probability Letters, Elsevier, vol. 111(C), pages 80-85.
    3. Dürre, Alexander & Vogel, Daniel, 2016. "Asymptotics of the two-stage spatial sign correlation," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 54-67.
    4. Dürre, Alexander & Vogel, Daniel & Tyler, David E., 2014. "The spatial sign covariance matrix with unknown location," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 107-117.
    5. Majumdar, Subhabrata & Chatterjee, Snigdhansu, 2022. "On weighted multivariate sign functions," Journal of Multivariate Analysis, Elsevier, vol. 191(C).
    6. Raymaekers, Jakob & Rousseeuw, Peter, 2019. "A generalized spatial sign covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 94-111.
    7. Alvarez, Agustín & Boente, Graciela & Kudraszow, Nadia, 2019. "Robust sieve estimators for functional canonical correlation analysis," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 46-62.
    8. C. Croux & C. Dehon & A. Yadine, 2010. "The k-step spatial sign covariance matrix," 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 137-150, September.
    9. Guangxing Wang & Sisheng Liu & Fang Han & Chong‐Zhi Di, 2023. "Robust functional principal component analysis via a functional pairwise spatial sign operator," Biometrics, The International Biometric Society, vol. 79(2), pages 1239-1253, June.
    10. Boente, Graciela & Rodriguez, Daniela & Sued, Mariela, 2019. "The spatial sign covariance operator: Asymptotic results and applications," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 115-128.
    11. Seija Sirkiä & Sara Taskinen & Hannu Oja & David Tyler, 2009. "Tests and estimates of shape based on spatial signs and ranks," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(2), pages 155-176.
    12. Debruyne, Michiel & Hubert, Mia & Van Horebeek, Johan, 2010. "Detecting influential observations in Kernel PCA," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3007-3019, December.
    13. Paindaveine, Davy & Van Bever, Germain, 2014. "Inference on the shape of elliptical distributions based on the MCD," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 125-144.
    14. Xu, Yangchang & Xia, Ningning, 2023. "On the eigenvectors of large-dimensional sample spatial sign covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 193(C).
    15. 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.
    16. Frahm, Gabriel, 2009. "Asymptotic distributions of robust shape matrices and scales," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1329-1337, August.
    17. Davy Paindaveine & Germain Van Bever, 2013. "Inference on the Shape of Elliptical Distribution Based on the MCD," Working Papers ECARES ECARES 2013-27, ULB -- Universite Libre de Bruxelles.
    18. Italo R. Lima & Guanqun Cao & Nedret Billor, 2019. "M-based simultaneous inference for the mean function of functional data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(3), pages 577-598, June.
    19. Bali, Juan Lucas & Boente, Graciela, 2015. "Influence function of projection-pursuit principal components for functional data," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 173-199.
    20. 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.

    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:eee:jmvana:v:135:y:2015:i:c:p:89-105. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.