The length heuristic for simultaneous hypothesis tests

Biometrika

Volumn 84, Issue 1, 1997, Pages 143-157

  Efron, Bradley ^a  

^a STANFORD UNIVERSITY   (United States)

Author keywords

O'brien fleming procedure; Repeated testing; Retelling; Two point bound; Volume of tubes

Indexed keywords

EID: 0000541612     PISSN: 00063444     EISSN: None     Source Type: Journal    
DOI: 10.1093/biomet/84.1.143     Document Type: Article

References (24)

1. BOHRER, R. & FRANCIS, G. (1972a). Sharp one-sided confidence bounds for linear regression over intervals. Biometrika 59, 99-108.
2. BOHRER, R. & FRANCIS, G. (1972b). Sharp one-sided confidence bounds over positive regions. Ann. Math. Statist. 43, 1541-48.
3. DAVIES, R. B. (1977). Hypothesis testing when a nuisance parameter is present only under the alternative. Biometrika 64, 247-54.
4. EFRON, B. (1969). Student's t-test under symmetry conditions. J. Am. Statist. Assoc. 64, 1278-302.
5. EFRON, B. (1988). Logistic regression, survival analysis, and the Kaplan-Meier curve. J. Am. Statist. Assoc. 83, 414-25.
6. FAIRBANKS, K. & MADSEN, R. (1982). P-values for tests using a repeated significant test design. Biometrika 69, 69-74.
7. HOPPE, F. M. (1985). Iterating Bonferroni bounds. Statist. Prob. Lett. 3, 121-5.
8. HOTELLING, H. (1939). Tubes and spheres in n-spaces, and a class of statistical problems Am. J. Math. 61, 440-60.
9. HUNTER, D. (1976). An upper bound for the probability of a union. J. Appl. Prob. 13, 597-603.
10. JOHANSEN, S. & JOHNSTONE, I. (1990). Hotelling's theorem on the volume of tubes: some illustrations in simultaneous inference and data analysis. Ann. Statist. 18, 652-84.
11. KNOWLES, M. & SIEGMUND, D. (1989). On Hotelling's geometric approach to testing for a nonlinear parameter in regression. Int. Statist. Rev. 57, 205-20.
12. MCCANN, M. & EDWARDS, D. (1996). A path length inequality for the Multivariate-t distribution, with applications to multiple comparisons. J. Am. Statist. Assoc. 91, 211-6.
13. MILLER, R. G., JR. (1981). Simultaneous Statistical Inference. New York: Springer-Verlag.
14. MILLER, R. G., JR. & SIEGMUND, D. (1982). Maximally selected chi-square statistics. Biometrics 38, 1011-6.
15. NAIMAN, D. Q. (1986). Conservative bands in curvilinear regression. Ann. Statist. 14, 896-906.
16. NAIMAN, D. Q. (1990). Volumes of tubular neighborhoods of spherical polyhedra and statistical inference. Ann. Statist. 18, 685-716.
17. NAIMAN, D. Q. & WYNN, H. P. (1992). Inclusion-exclusion-Bonferroni identities and inequalities for discrete tube-like problems via Euler characteristics. Ann. Statist. 20, 43-76.
18. O'BRIEN, P. C. & FLEMING, T. R. (1979). A multiple testing procedure for clinical trials. Biometrics 35, 549-56.
19. PETROSIAN, V. & EFRON, B. (1995). On the correlation of angular position with time of occurrence of gamma-ray bursts. Astrophys. J. Lett. 441, L37-38.
20. POCOCK, S. J. (1977). Group sequential methods in the design and analysis of clinical trials. Biometrika 64, 191-9.
21. POCOCK, S. J. (1979). Allocation of patients to treatment in clinical trials. Biometrics 35, 183-97.
22. TOMESCU, I. (1984). Hypertrees and Bonferroni inequalities. J. Combinat. Theory B 41, 209-17.
23. WORSLEY, K. J. (1982). An improved Bonferroni inequality and applications. Biometrika 69, 297-302.
24. WORSLEY, K. J. (1985). Bonferroni (improved) wins again. Am. Statistician 39, 235.