On the efficiency of multivariate spatial sign and rank tests

Annals of Statistics

Volumn 25, Issue 2, 1997, Pages 542-552

  Möttönen, Jyrki ^a   Oja, Hannu ^a   Tienari, Juha ^a  

^a UNIVERSITY OF OULU   (Finland)

Author keywords

Angle test; Asymptotic efficiency; Multivariate location; Multivariate rank test; Multivariate sign test; Spatial median

Indexed keywords

EID: 0031490487     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1031833663     Document Type: Article

References (24)

1. BILLINGSLEY, P. (1968). Convergence of Probability Measures. Wiley, New York.
2. BROWN, B. M. (1983). Statistical uses of the spatial median. J. Roy. Statist. Soc. Ser. B 45 25-30.
3. BROWN, B. M. and HETTMANSPERGER, T. P. (1989). An affine invariant bivariate version of the sign test. J. Roy. Statist. Soc. Ser. B 51 117-125.
4. BROWN, B. M., HETTMANSPERGER, T. P., NYBLOM, J. and OJA, H. (1992). On certain bivariate sign tests and medians. J. Amer. Statist. Assoc. 87 127-135.
5. CHAUDHURI, P. (1992). Multivariate location estimation using extension of R-estimates through U-statistics type approach. Ann. Statist. 20 897-916.
6. 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.
7. ERDÉLYI, A., MAGNUS, W., OBERHETTINGER, F. and TRICOMI, F. G. (1953). Higher Transcendental Functions 1. McGraw-Hill, New York.
8. HAJEK, J. and SIDÁK, Z. (1967). Theory of Rank Tests. Academic Press, New York.
9. HETTMANSPERGER, T. P. and AUBUCHON, J. C. (1988). Comment on "Rank-based robust analysis of linear models. I. Exposition and review by David Draper. Statist. Sci. 3 262-263.
10. 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.
11. JAN, S.-L. and HANDLES, R. H. (1994). A multivariate signed sum test for the one-sample location problem. J. Nonparametr. Statist. 4 49-63.
12. JOHNSON, N. L. and KOTZ, S. (1972). Distributions in Statistics 4. Continuous Multivariate Distributions. Wiley, New York.
13. LEHMANN, E. L. (1983). Theory of Point Estimation. Wiley, New York.
14. MÖTTÖNEN, J. and OJA, H. (1994). Efficiency of the spatial signed-rank test. Unpublished manuscript.
15. MÖTTÖNEN, J. and OJA, H. (1995). Multivariate spatial sign and rank methods. J. Nonparametr. Statist. 5 201-213.
16. OJA, H. (1983). Descriptive statistics for multivariate distributions. Statist. Probab. Lett. 1 327-332.
17. OJA, H. and NIINIMAA, A. (1985). Asymptotic properties of the generalized median in the case of multivariate normality. J. Roy. Statist. Soc. Ser. B 47 372-377.
18. OJA, H. and NYBLOM, J. (1989). On bivariate sign tests. J. Amer. Statist. Assoc. 84 249-259.
19. RANDLES, R. H. (1989). A distribution-free multivariate sign test based on interdirections. J. Amer. Statist. Assoc. 84 1045-1050.
20. 1-Statistical Analysis and Related Methods (Y. Dodge, ed.) 295-302. North-Holland, Amsterdam.
21. HANDLES, R. H. and PETERS, D. (1990). Multivariate rank tests for the two-sample location problem. Comm. Statist. Theory Methods 19 4225-4238.
22. RANGA RAO, R. (1962). Relations between weak and uniform convergence of measures with applications. Ann. Math. Statist. 33 659-680.
23. SERFLING, R. J. (1980). Approximation Theorems of Mathematical Statistics. Wiley, New York.
24. SHORACK, G. R. and WELLNER, J. A. (1986). Empirical Processes with Applications to Statistics. Wiley, New York.