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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
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    References listed on IDEAS

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    1. Thomas P. Hettmansperger, 2002. "A practical affine equivariant multivariate median," Biometrika, Biometrika Trust, vol. 89(4), pages 851-860, December.
    2. Lounasheimo, Antton, 1999. "The Impact of Human Capital on Economic Growth," Discussion Papers 673, The Research Institute of the Finnish Economy.
    3. 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.
    4. 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.
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    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. 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.
    8. 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.
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    11. Julie A. Stoner, 2002. "Analysis of clustered data: A combined estimating equations approach," Biometrika, Biometrika Trust, vol. 89(3), pages 567-578, August.
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    Cited by:

    1. Majumdar, Subhabrata & Chatterjee, Snigdhansu, 2022. "On weighted multivariate sign functions," Journal of Multivariate Analysis, Elsevier, vol. 191(C).
    2. 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.
    3. 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.

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