A weighted spatial median for clustered data

Statistical Methods and Applications

Volumn 15, Issue 3, 2007, Pages 355-379

  Nevalainen, Jaakko ^a   Larocque, Denis ^b   Oja, Hannu ^c  

^a TAMPERE UNIVERSITY OF TECHNOLOGY   (Finland)

^b HEC MONTRÉAL   (Canada)

^c UNIVERSITY OF TAMPERE   (Finland)

Author keywords

Breakdown point; Clustered data; Intracluster correlation; Multivariate one sample location problem; Sign correlation; Spatial median

Indexed keywords

EID: 33846663949     PISSN: 16182510     EISSN: 1613981X     Source Type: Journal    
DOI: 10.1007/s10260-006-0031-7     Document Type: Article

References (32)

1. Abramowitz M, Stegun EI (eds) (1970) Handbook of mathematical functions. Dover, New York
2. Azzalini A, Capitanio A (1999) Statistical applications of the multivariate skew-normal distribution. J R Stat Soc Ser B 61:579-602
3. Bramati MC, Croux C (2006) Robust estimators for the fixed effects panel data model. Under revision
4. Brown BM (1983) Statistical uses of the spatial median. J R Statist Soc Ser B 45:25-30
5. Chakraborty B, Chaudhuri P (1996) On a transformation and re-transformation technique for constructing affine equivariant multivariate median. In: Proceedings of the American mathematical society vol 124, pp 2539-2547
6. Chakraborty B, Chaudhuri P, Oja H (1998) Operating transformation retransformation on spatial median and angle test. Statistica Sinica 8:767-784
7. Datta S, Satten GA (2005) Rank-sum tests for clustered data. J Am Statist Assoc 100:908-915
8. Davies PL, Gather U (2005) Breakdown and groups (with discussion). Ann Statist 33:977-1035
9. Donoho DL, Huber PJ (1983) The notion of breakdown point. In: Bickel PJ, Doksum KA, Hodges JL Jr (eds) A Festschrift for Erich L. Lehmann. Wadsworth, Belmont, California, pp 157-184
10. Dümbgen L (1998) On Tyler's M-functional of scatter in high dimension. Ann Inst Statist Math 50:471-491
11. Genton MG, Lucas A (2003) Comprehensive definitions of breakdown points for independent and dependent observations. J R Statist Soc Ser B 65:81-94
12. Hettmansperger TP, McKean JW (1998) Robust nonparametric statistical methods. Arnold, London
13. Hettmansperger TP, Randles RH (2002) A practical affine equivariant multivariate median. Biometrika 89:851-860
14. Larocque D (2003) An affine-invariant multivariate sign test for cluster correlated data. Can J Statist 31:437-455
15. Larocque D (2005) The Wilcoxon signed-rank test for cluster correlated data. In: Duchesne P, Rémillard B (eds) Statistical modeling and analysis for complex data problems. Springer, Berlin Heidelberg New York, pp 309-323
16. Larocque D, Nevalainen J, Oja H (2007) A weighted multivariate sign test for cluster correlated data. Biometrika (in press)
17. Lopuhaä HP, Rousseeuw PJ (1991) Breakdown points of affine equivariant estimators of multivariate location and covariance matrices. Ann Statist 19:229-248
18. Möttönen J, Oja H, Tienari J (1997) On the efficiency of multivariate spatial sign and rank tests. Ann Statist 25:542-552
19. Müller CH, Uhlig S (2001) Estimation of variance components with high breakdown point and high efficiency. Biometrika 88:353-366
20. Nevalainen J, Larocque D, Oja H (2007) The multivariate spatial median for clustered data. Can J Statist (in press)
21. Oja H, Randles RH (2004) Multivariate nonparametric tests. Statist Sci 19:598-605
22. R Development Core Team (2004) R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL http://www.R-project.org. ISBN 3-900051-00-3
23. Randles RH (2000) A simpler, affine-invariant, multivariate, distribution-free sign test. J Am Statist Assoc 95:1263-1268
24. Rosner B, Grove D (1999) Use of the Mann-Whitney U-test for clustered data. Statist Med 18: 1387-1400
25. Rosner B, Glynn RJ, Ting Lee M-L (2003) Incorporation of clustering effects for the Wilcoxon rank sum test: a large sample approach. Biometrics 59:1089-1098
26. Saw JG (1983) Dependent unit vectors. Biometrika 70:665-671
27. Serfling RJ (1980) Approximation theorems of mathematical statistics. Wiley, New York
28. Stoner JA, Leroux BG (2002) Analysis of clustered data: a combined estimating equations approach. Biometrika 89:567-578
29. Taskinen S, Croux C, Kankainen A, Ollila E, Oja H (2006) Influence functions and efficiencies fo the canonical correlation and vector estimates based on scatter and shape matrices. J Multivariate Anal 97:359-384
30. Tyler DE (1987) A distribution-free M-estimator of multivariate scatter. Ann Statist 15:234-251
31. Vardi Y, Zhang C-H (2001) A modified Weiszfeld algorithm for the Fermat-Weber location problem. Math Program Ser A 90:559-566
32. Williamson JM, Datta S, Satten GA (2003) Marginal analyses of clustered data when cluster size is informative. Biometrics 59:36-42