The geometry of the affine invariant multivariate sign and rank methods

Journal of Nonparametric Statistics

Volumn 11, Issue 1-3, 1999, Pages 271-285

  Hettmansperger, T P ^a   Mottonen J ^b   Oja, H ^b  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

^b UNIVERSITY OF OULU   (Finland)

Author keywords

Hyperplane; L1 methods; Multivariate median; Multivariate rank test; Multivariate sign test; Robustness

Indexed keywords

EID: 0042213941     PISSN: 10485252     EISSN: None     Source Type: Journal    
DOI: 10.1080/10485259908832784     Document Type: Article

References (16)

1. Chaudhuri, P. and Sengupta, D. (1993) Sign tests in multidimension: Inference based on the geometry of the data cloud, J. Amer. Statist. Assoc., 88, 1363-1370.
2. Donoho, D. L. (1982) Breakdown properties of multivariate location estimators, Ph.D. Qualifying Paper, Harvard University, Boston, MA.
3. Hampel, F., Ronchetti, E. M., Rousseeuw, P. and Stahel, W. A. (1986) Robust Statistics. The Approach Based on Influence Functions, Wiley, New York.
4. Hettmansperger, T. P., Möttönen, J. and Oja, H. (1997) Affine invariant multivariate one-sample signed-rank tests. J. Amer. Statist. Assoc., 92, 1591-1600.
5. Hettmansperger, T. P., Möttönen, J. and Oja, H. (1998) Affine invariant multivariate two-sample rank tests. Statistica Sinica, 8, 785-800.
6. Hettmansperger, T. P., Nyblom, J. and Oja, H. (1994) Affine invariant multivariate one-sample sign tests, J. Roy. Statist. Soc. Ser. B, 56, 221-234.
7. Hettmansperger, T. P. and Oja, H. (1994) Affine invariant multivariate multisample sign tests, J. Roy. Statist. Soc. Ser. B, 56, 235-249.
8. Jan, S.-L. and Randles, R. H. (1996) Interdirection tests for simple repeated measures designs, J. Amer. Statist. Assoc., 91, 1611-1618.
9. Liu, R. Y. (1990) On a Notion of Data Depth Based upon Random Simplices, Ann. Statist., 18, 405-414.
10. Niinimaa, A., Oja, H. and Nyblom, J. (1992) Algorithm AS 277: The Oja Bivariate Median, Appl. Statist., 41, 611-617.
11. Randles, R. H. (1989) A distribution-free multivariate sign test based on interdirections, J. Amer. Statist. Assoc., 84, 1045-1050.
12. Rousseeuw, P. J. and Bassett, G. W.Jr. (1991) Robustness of the p-subset algorithm for regression with high breakdown point. In: Directions in Robust Statistics and Diagnostics: Part II, Stahel W. and Weisberg S. Eds., 185-194, Springer-Verlag, New York.
13. Rousseeuw, P. J. and Leroy, A. M. (1987) Robust Regression and Outlier Detection, John Wiley, New York.
14. Rousseeuw, P. J. and van Zomern, B. C. (1990) Unmasking multivariate outliers and leverage points (with discussion), J. Amer. Statist. Assoc., 85, 633-651.
15. Ruppert, D. (1992) Computing S estimators for regression and multivariate location/ dispersion, J. Computational and Graphical Statistics, 1, 253-270.
16. Stahel, W. A. (1981) Robuste Schätzungen: Infinitesimale Optimalität und Schätzungen von Kovarianzmatrizen, Ph.D. Thesis, ETH Zürich, Schwitzerland.