Exact and approximate stepdown methods for multiple hypothesis testing

Journal of the American Statistical Association

Volumn 100, Issue 469, 2005, Pages 94-108

  Romano, Joseph P ^a   Wolf, Michael ^b  

^a STANFORD UNIVERSITY   (United States)

^b UNIVERSITAT POMPEU FABRA   (Spain)

Author keywords

Bootstrap; Familywise error rate; Multiple testing; Permutation test; Randomization test; Stepdown procedure; Subsampling

Indexed keywords

EID: 14944362897     PISSN: 01621459     EISSN: None     Source Type: Journal    
DOI: 10.1198/016214504000000539     Document Type: Article

References (33)

1. Aitken, M. (1969), "Some Tests for Correlation Matrices," Biometrika, 56, 443-446.
2. _ (1971), Correction to "Some Tests for Correlation Matrices," Biometrika, 58, 245.
3. Benjamini, Y., and Hochberg, Y. (1995), "Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing," Journal of the Royal Statistical Society, Ser. B, 57, 289-300.
4. Benjamini, Y., and Yekutieli, D. (2001), "The Control of the False Discovery Rate in Multiple Testing Under Dependency," The Annals of Statistics, 29, 1165-1188.
5. Beran, R. (1986), "Simulated Power Functions," The Annals of Statistics, 14, 151-173.
6. _ (1988a), "Balanced Simultaneous Confidence Sets," Journal of the American Statistical Association, 83, 679-686.
7. _ (1988b), "Prepivoting Test Statistics: A Bootstrap View of Asymptotic Refinements," Journal of the American Statistical Association, 83, 687-697.
8. Bertail, P., Politis, D., and Romano, J. (1999), "On Subsampling Estimators With Unknown Rate of Convergence," Journal of the American Statistical Association, 94, 569-579.
9. Dudoit, S., Shaffer, J., and Boldrick, J. (2003), "Multiple Hypothesis Testing in Microarray Experiments," Statistical Science, 18, 71-103.
10. Finner, H. (1999), "Stepwise Multiple Test Procedures and Control of Directional Errors," The Annals of Statistics, 27, 274-289.
11. Finner, H., and Roters, M. (1998), "Asymptotic Comparison of Step-Down and Step-Up Multiple Test Procedures Based on Exchangeable Test Statistics," The Annals of Statistics, 26, 505-524.
12. Hall, P. (1992), The Bootstrap and Edgeworth Expansion, New York: Springer-Verlag.
13. Hall, P., and Wilson, S. (1991), "Two Guidelines for Bootstrap Hypothesis Testing," Biometrics, 47, 757-762.
14. Hochberg, Y., and Tamhane, A. (1987), Multple Comparison Procedures, New York: Wiley.
15. Hoeffding, W. (1952), "The Large-Sample Power of Tests Based on Permutations of Observations," The Annals of Mathematical Statistics, 23, 169-192.
16. Holm, S. (1979), "A Simple Sequentially Rejective Multiple Test Procedure," Scandinavian Journal of Statistics, 6, 65-70.
17. Hommel, G. (1986), "Multiple Test Procedures for Arbitrary Dependence Structures," Metrika, 33, 321-336.
18. Kim, J., and Pollard, D. B. (1990), "Cube Root Asymptotics," The Annals of Statistics, 18, 191-219.
19. Lahiri, S. N. (2003), Resampling Methods for Dependent Data, New York: Springer-Verlag.
20. Lehmann, E., Romano, J. P., and Shaffer, J. (2003), "On Optimality of Stepdown and Stepup Multiple Test Procedures," Technical Report 2003-12, Stanford University, Dept. of Statistics.
21. Marcus, R., Peritz, E., and Gabriel, K. (1976), "On Closed Testing Procedures With Special Reference to Ordered Analysis of Variance," Biometrika, 63, 655-660.
22. Petrondas, D., and Gabriel, K. (1983), "Multiple Comparisons by Rerandomization Tests," Journal of the American Statistical Association, 78, 949-957.
23. Politis, D. N., Romano, J. P., and Wolf, M. (1999), Subsampling, New York: Springer-Verlag.
24. Rodríguez-Poo, J., Delgado, M., and Wolf, M. (2001), "Subsampling Inference in Cube Root Asymptotics With an Application to Manski's Maximum Score Estimator," Economies Letters, 73, 241-250.
25. Rogers, J., and Hsu, J. (2001), "Multiple Comparisons of Biodiversity," Biometrical Journal, 43, 617-625.
26. Romano, J. (1988), "A Bootstrap Revival of Some Nonparametric Distance Tests," Journal of the American Statistical Association, 83, 698-708.
27. _ (1989), "Bootstrap and Randomization Tests of Some Nonparametric Hypotheses," The Annals of Statistics, 17, 141-159.
28. _ (1990), "On the Behavior of Randomization Tests Without a Group Invariance Assumption," Journal of the American Statistical Association, 85, 686-692.
29. Troendle, J. (1995), "A Stepwise Resampling Method of Multiple Hypothesis Testing," Journal of the American Statistical Association, 90, 370-378.
30. Tu, W., and Zhou, X. (2000), "Pairwise Comparison of the Means of Skewed Data," Journal of Statistical Planning and Inference, 88, 59-74.
31. Westfall, P. H., and Wolfinger, R. D. (1997), "Multiple Tests With Discrete Distributions," The American Statistician, 51, 3-8.
32. Westfall, P. H., and Young, S. S. (1993), Resampling-Based Multiple Testing: Examples and Methods for P-Value Adjustment, New York: Wiley.
33. Westfall, P. H., Zaykin, D. V., and Young, S. S. (2001), "Multiple Tests for Genetic Effects in Association Studies," in Methods in Molecular Biology: Biostatistical Methods, Vol. 184, ed. S. Looney, Toloway, NJ: Humana Press, pp. 143-168.