Maximal asymptotic power and efficiency of two-sample tests based on generalized U-Statistics

Metrika

Volumn 60, Issue 1, 2004, Pages 33-57

  Ferger, Dietmar ^a  

^a DRESDEN UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Maximal local power; Optimal asymptotic relative efficiency; Statistical functionals; Two sample U Statistics

Indexed keywords

EID: 17444361849     PISSN: 00261335     EISSN: None     Source Type: Journal    
DOI: 10.1007/s001840300295     Document Type: Article

References (29)

1. 2-norm of multivariate probability density functions. Nonparametric Statist. 2:169-181
2. Bahr R (1996) A new test for the multi-dimensional two-sample problem with general alternatives. Doctoral thesis, University of Hannover. [In German]
3. Bhapkar VP (1961) A nonparametric test for the problem of several samples. Ann. Math. Statist. 32:1108-1117
4. Bickel PJ, Klaassen CAJ, Ritov Y, Wellner JA (1993) Efficient and adaptive estimation for semiparametric models. The Johns Hopkins University Press, Baltimore and London
5. Deshpande JV (1963) A nonparametric test based on U-statistics for several samples. Abstract Ann. Math. Statist. 34:1624
6. Deshpande JV (1964) Multisample nonparametric tests for equality of scales. Abstract Ann. Math. Statist. 35:937
7. m and scanning martingales. IMS Monographs / Lecture Notes 36. Festschrift for Willem R. van Zwet, 434-464
8. Epps TW, Singleton KJ (1986) An omnibus test for the two-sample problem using the empirical characteristic function. J. Statist. Comput. Simul. 26:177-203
9. Ferger D (1994) On the power of nonparametric change-point tests. Metrika 41:277-292
10. Ferger D (2000) Optimal tests for the general two-sample problem. J. Multivariate Anal. 74:1-35
11. Ferger D (2001) Linear statistics with estimated score-functions for the two-sample problem. Manuscript. Dresden University of Technology
12. Hájek J, Sidák Z, Sen PK (1999) Theory of rank tests (Second Edition) Academic Press, New York
13. Henze N (1988) A multivariate two-sample test based on the number of nearest neigbor type coincidences. 16:772-783
14. Henze N, Penrose MD (1999) On the multivariate runs test. Ann. Statist. 27:290-298
15. Hettmansperger TP, McKean JW (1998) Robust nonparametric statistical methods. Kendall's library of statistics 5, Wiley, New York
16. Janssen A (1999) Testing nonparametric statistical functionals with applications to rank tests. J. Statist. Planning Inference 81:71-93
17. Koroljuk VS, Borovskich YuV (1994) Theory of U-Statistics. Kluwer Academic Publishers, Dordrecht
18. Lee AJ (1990) U-Statistics. Marcel Dekker, New York
19. Lehmann EL (1986) Testing statistical hypothesis. (Second Edition) Springer-Verlag, New York
20. Lehmann EL (1999) Elements of large-sample theory. Springer-Verlag, New York
21. Pfanzagl J (with the assistance of W. Wefelmeyer) (1982) Contributions to a general asymptotic statistical theory. Lecture Notes in Statist. 13. Springer-Verlag, New York
22. Pfanzagl J (with the assistance of W. Wefelmeyer) (1985) Asymptotic Expansions for general statistical models. Lecture Notes in Statist. 31. Springer-Verlag, New York
23. Ramsay JO, Silverman BW (1997) Functional data analysis. Springer-Verlag, New York
24. Serfling RJ (1980) Approximation theorems of mathematical statistics. Wiley, New York
25. Sugiura N (1965) Multisample and multivariate nonparametric tests based on U-statistics and their asymptotic efficiencies. Osaka J. Math. 2:385-426
26. Sukhatme BV (1957) On certain two-sample non-parametric tests for variances. Ann. Math. Statist. 28:188-194
27. Tamura R (1958) On a nonparametric two-sample test for scale. The Scientific Reports of the Shimane Univ. 8:1-8
28. Tamura R (1960) On the nonparametric tests based on certain U-statistics. Bull. Math. Stat. 9:61-67
29. Witting H, Müller-Funk U (1995) Mathematische Statistik II. B. G. Teubner, Stuttgart