IDEAS home Printed from https://ideas.repec.org/a/spr/stmapp/v15y2007i3d10.1007_s10260-006-0031-7.html
   My bibliography  Save this article

A weighted spatial median for clustered data

Author

Listed:
  • Jaakko Nevalainen

    (University of Tampere)

  • Denis Larocque

    (HEC Montréal 3000 chemin de la Côte-Sainte-Catherine, Montréal (Québec))

  • Hannu Oja

    (University of Tampere)

Abstract

A weighted spatial median is proposed for the multivariate one-sample location problem with clustered data. Its limiting distribution is derived under mild conditions (no moment assumptions) and it is shown to be multivariate normal. Asymptotic as well as finite sample efficiencies and breakdown properties are considered, and the theoretical results are supplied with illustrative examples. It turns out that there is a potential for meaningful gains in estimation efficiency: the weighted spatial median has superior efficiency to the unweighted spatial median particularly when the cluster sizes are widely disparate and in the presence of strong intracluster correlation. The unweighted spatial median for clustered data was considered earlier by Nevalainen et al. (Can J Statist, in press, 2007). The proposed weighted estimators provide companion estimates to the weighted affine invariant sign test proposed recently by Larocque et al. (Biometrika, in press, 2007). An affine equivariant weighted spatial median is discussed in parallel.

Suggested Citation

  • Jaakko Nevalainen & Denis Larocque & Hannu Oja, 2007. "A weighted spatial median for clustered data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 15(3), pages 355-379, February.
    • Handle: RePEc:spr:stmapp:v:15:y:2007:i:3:d:10.1007_s10260-006-0031-7
    DOI: 10.1007/s10260-006-0031-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10260-006-0031-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10260-006-0031-7?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. Datta, Somnath & Satten, Glen A., 2005. "Rank-Sum Tests for Clustered Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 908-915, September.
    2. A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
    3. Julie A. Stoner, 2002. "Analysis of clustered data: A combined estimating equations approach," Biometrika, Biometrika Trust, vol. 89(3), pages 567-578, August.
    4. Lounasheimo, Antton, 1999. "The Impact of Human Capital on Economic Growth," Discussion Papers 673, The Research Institute of the Finnish Economy.
    5. Denis Larocque & Jaakko Nevalainen & Hannu Oja, 2007. "A weighted multivariate sign test for cluster-correlated data," Biometrika, Biometrika Trust, vol. 94(2), pages 267-283.
    6. John M. Williamson & Somnath Datta & Glen A. Satten, 2003. "Marginal Analyses of Clustered Data When Cluster Size Is Informative," Biometrics, The International Biometric Society, vol. 59(1), pages 36-42, March.
    7. 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.
    8. Marc G. Genton & André Lucas, 2003. "Comprehensive definitions of breakdown points for independent and dependent observations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 81-94, February.
    9. Thomas P. Hettmansperger, 2002. "A practical affine equivariant multivariate median," Biometrika, Biometrika Trust, vol. 89(4), pages 851-860, December.
    10. ., 1999. "The assessment of capital adequacy," Chapters, in: Handbook of Banking Regulation and Supervision in the United Kingdom, chapter 17, Edward Elgar Publishing.
    11. Bernard Rosner & Robert J. Glynn & Mei-Ling Ting Lee, 2003. "Incorporation of Clustering Effects for the Wilcoxon Rank Sum Test: A Large-Sample Approach," Biometrics, The International Biometric Society, vol. 59(4), pages 1089-1098, December.
    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. Majumdar, Subhabrata & Chatterjee, Snigdhansu, 2022. "On weighted multivariate sign functions," Journal of Multivariate Analysis, Elsevier, vol. 191(C).
    2. Janice L. Scealy & David Heslop & Jia Liu & Andrew T. A. Wood, 2022. "Directions Old and New: Palaeomagnetism and Fisher (1953) Meet Modern Statistics," International Statistical Review, International Statistical Institute, vol. 90(2), pages 237-258, August.
    3. Haataja, Riina & Larocque, Denis & Nevalainen, Jaakko & Oja, Hannu, 2009. "A weighted multivariate signed-rank test for cluster-correlated data," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1107-1119, July.

    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. Jaakko Nevalainen & Denis Larocque & Hannu Oja, 2007. "A weighted spatial median for clustered data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 15(3), pages 355-379, February.
    2. Omer Ozturk & Asuman Turkmen, 2016. "Quantile inference based on clustered data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(7), pages 867-893, October.
    3. Jaakko Nevalainen & Somnath Datta & Hannu Oja, 2014. "Inference on the marginal distribution of clustered data with informative cluster size," Statistical Papers, Springer, vol. 55(1), pages 71-92, February.
    4. David Mayston, 2015. "Analysing the effectiveness of public service producers with endogenous resourcing," Journal of Productivity Analysis, Springer, vol. 44(1), pages 115-126, August.
    5. Olcay Arslan, 2015. "Variance-mean mixture of the multivariate skew normal distribution," Statistical Papers, Springer, vol. 56(2), pages 353-378, May.
    6. Mehdi Amiri & Ahad Jamalizadeh & Mina Towhidi, 2015. "Inference and further probabilistic properties of the $$ SUN_{n,2}$$ S U N n , 2 -distribution," Statistical Papers, Springer, vol. 56(4), pages 1071-1098, November.
    7. Hea-Jung Kim, 2015. "A best linear threshold classification with scale mixture of skew normal populations," Computational Statistics, Springer, vol. 30(1), pages 1-28, March.
    8. Denis Larocque & Riina Haataja & Jaakko Nevalainen & Hannu Oja, 2010. "Two sample tests for the nonparametric Behrens–Fisher problem with clustered data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(6), pages 755-771.
    9. Tsung-I Lin & Pal Wu & Geoffrey McLachlan & Sharon Lee, 2015. "A robust factor analysis model using the restricted skew- $$t$$ t distribution," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 510-531, September.
    10. Wan-Lun Wang & Tsung-I Lin, 2015. "Robust model-based clustering via mixtures of skew-t distributions with missing information," 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. 9(4), pages 423-445, December.
    11. Anna Gottard & Simona Pacillo, 2007. "On the impact of contaminations in graphical Gaussian models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 15(3), pages 343-354, February.
    12. You-Gan Wang & Yudong Zhao, 2008. "Weighted Rank Regression for Clustered Data Analysis," Biometrics, The International Biometric Society, vol. 64(1), pages 39-45, March.
    13. Wan-Lun Wang & Min Liu & Tsung-I Lin, 2017. "Robust skew-t factor analysis models for handling missing data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(4), pages 649-672, November.
    14. Liya Fu & You-Gan Wang, 2012. "Efficient Estimation for Rank-Based Regression with Clustered Data," Biometrics, The International Biometric Society, vol. 68(4), pages 1074-1082, December.
    15. Somnath Datta & Jaakko Nevalainen & Hannu Oja, 2012. "A general class of signed-rank tests for clustered data when the cluster size is potentially informative," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(3), pages 797-808.
    16. Haataja, Riina & Larocque, Denis & Nevalainen, Jaakko & Oja, Hannu, 2009. "A weighted multivariate signed-rank test for cluster-correlated data," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1107-1119, July.
    17. Riina Lemponen & Denis Larocque & Jaakko Nevalainen & Hannu Oja, 2012. "Weighted rank tests and Hodges-Lehmann estimates for the multivariate two-sample location problem with clustered data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(4), pages 977-991, December.
    18. Nadia Solaro & Alessandro Barbiero & Giancarlo Manzi & Pier Alda Ferrari, 2017. "A sequential distance-based approach for imputing missing data: Forward Imputation," 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. 11(2), pages 395-414, June.
    19. Prates, Marcos Oliveira & Lachos, Victor Hugo & Barbosa Cabral, Celso Rômulo, 2013. "mixsmsn: Fitting Finite Mixture of Scale Mixture of Skew-Normal Distributions," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 54(i12).
    20. Camila Zeller & Victor Lachos & Filidor Labra, 2014. "Influence diagnostics for Grubbs’s model with asymmetric heavy-tailed distributions," Statistical Papers, Springer, vol. 55(3), pages 671-690, August.

    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:spr:stmapp:v:15:y:2007:i:3:d:10.1007_s10260-006-0031-7. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.