Exact and asymptotically robust permutation tests

Annals of Statistics

Volumn 41, Issue 2, 2013, Pages 484-507

  Chung, Eunyi ^a   Romano, Joseph P ^a  

^a STANFORD UNIVERSITY   (United States)

Author keywords

Behrens Fisher problem; Coupling; Permutation test

Indexed keywords

EID: 84879136073     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/13-AOS1090     Document Type: Article

References (24)

1. CHUNG, E. and ROMANO, P. J. (2011). Asymptotically valid and exact permutation tests based on two-sample U-statistics. Technical Report 2011-09, Dept. Statistics, Stanford Univ.
2. CHUNG, E. and ROMANO, P. J. (2013). Supplement to "Exact and asymptotically robust permutation tests." DOI:10.1214/13-AOS1090SUPP.
3. DELAIGLE, A., HALL, P. and JIN, J. (2011). Robustness and accuracy of methods for high dimensional data analysis based on Student's t -statistic. J. R. Stat. Soc. Ser. B Stat. Methodol. 73 283-301. MR2815777.
4. DEVROYE, L. P. and WAGNER, T. J. (1980). The strong uniform consistency of kernel density estimates. In Multivariate Analysis, V (Proc. Fifth Internat. Sympos., Univ. Pittsburgh, Pittsburgh, Pa., 1978) 59-77. North-Holland, Amsterdam. MR0566330.
5. EFRON, B. (1979). Bootstrap methods: Another look at the jackknife. Ann. Statist. 7 1-26. MR0515681.
6. HALL, P., DICICCIO, T. J. and ROMANO, J. P. (1989). On smoothing and the bootstrap. Ann. Statist. 17 692-704. MR0994260.
7. HALL, P. and WILSON, S. R. (1991). Two guidelines for bootstrap hypothesis testing. Biometrics 47 757-762. MR1132543.
8. HOEFFDING, W. (1952). The large-sample power of tests based on permutations of observations. Ann. Math. Statist. 23 169-192. MR0057521.
9. JANSSEN, A. (1997). Studentized permutation tests for non-i.i.d. hypotheses and the generalized Behrens-Fisher problem. Statist. Probab. Lett. 36 9-21. MR1491070.
10. JANSSEN, A. (1999). Testing nonparametric statistical functionals with applications to rank tests. J. Statist. Plann. Inference 81 71-93. MR1718393.
11. JANSSEN, A. (2005). Resampling Student's t-type statistics. Ann. Inst. Statist. Math. 57 507- 529. MR2206536.
12. JANSSEN, A. and PAULS, T. (2003). How do bootstrap and permutation tests work? Ann. Statist. 31 768-806. MR1994730.
13. JANSSEN, A. and PAULS, T. (2005). A Monte Carlo comparison of studentized bootstrap and permutation tests for heteroscedastic two-sample problems. Comput. Statist. 20 369-383. MR2242115.
14. JANSSEN, A. and PAULY, M. (2009). Asymptotics and effectiveness of conditional tests with applications to randomization tests. Technical report, Univ. Duesseldorf.
15. KRISHNAMOORTHY, K., LU, F. and MATHEW, T. (2007). A parametric bootstrap approach for ANOVA with unequal variances: Fixed and random models. Comput. Statist. Data Anal. 51 5731-5742. MR2407673.
16. LEHMANN, E. L. and ROMANO, J. P. (2005). Testing Statistical Hypotheses, 3rd ed. Springer, New York. MR2135927.
17. NEUBERT, K. and BRUNNER, E. (2007). A studentized permutation test for the non-parametric Behrens-Fisher problem. Comput. Statist. Data Anal. 51 5192-5204. MR2370717.
18. NEUHAUS, G. (1993). Conditional rank tests for the two-sample problem under random censorship. Ann. Statist. 21 1760-1779. MR1245767.
19. OMELKA, M. and PAULY, M. (2012). Testing equality of correlation coefficients in a potentially unbalanced two-sample problem via permutation methods. J. Statist. Plann. Inference 142 1396-1406.
20. PAULY, M. (2011). Discussion about the quality of F-ratio resampling tests for comparing variances. TEST 20 163-179. MR2806315.
21. RICE, W. R. and GAINES, S. D. (1989). One-way analysis of variance with unequal variances. Proc. Natl. Acad. Sci. USA 86 8183-8184. MR1021453.
22. ROMANO, J. P. (1989). Bootstrap and randomization tests of some nonparametric hypotheses. Ann. Statist. 17 141-159. MR0981441.
23. ROMANO, J. P. (1990). On the behavior of randomization tests without a group invariance assumption. J. Amer. Statist. Assoc. 85 686-692. MR1138350.
24. SERFLING, R. J. (1980). Approximation Theorems of Mathematical Statistics. Wiley, New York. MR0595165.