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A weighted multivariate sign test for cluster-correlated data

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  • Denis Larocque
  • Jaakko Nevalainen
  • Hannu Oja

Abstract

We consider the multivariate location problem with cluster-correlated data. A family of multivariate weighted sign tests is introduced for which observations from different clusters can receive different weights. Under weak assumptions, the test statistic is asymptotically distributed as a chi-squared random variable as the number of clusters goes to infinity. The asymptotic distribution of the test statistic is also given for a local alternative model under multivariate normality. Optimal weights maximizing Pitman asymptotic efficiency are provided. These weights depend on the cluster sizes and on the intracluster correlation. Several approaches for estimating these weights are presented. Using Pitman asymptotic efficiency, we show that appropriate weighting can increase substantially the efficiency compared to a test that gives the same weight to each cluster. A multivariate weighted t-test is also introduced. The finite-sample performance of the weighted sign test is explored through a simulation study which shows that the proposed approach is very competitive. A real data example illustrates the practical application of the methodology. Copyright 2007, Oxford University Press.

Suggested Citation

  • 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.
  • Handle: RePEc:oup:biomet:v:94:y:2007:i:2:p:267-283
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    File URL: http://hdl.handle.net/10.1093/biomet/asm026
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    1. repec:spr:stmapp:v:15:y:2007:i:3:d:10.1007_s10260-006-0031-7 is not listed on IDEAS
    2. Janie McDonald & Patrick D. Gerard & Christopher S. McMahan & William R. Schucany, 2016. "Exact-Permutation-Based Sign Tests for Clustered Binary Data Via Weighted and Unweighted Test Statistics," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(4), pages 698-712, December.
    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.
    4. 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.
    5. Paindaveine, Davy, 2009. "On Multivariate Runs Tests for Randomness," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1525-1538.
    6. 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.
    7. 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.

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