Some probability inequalities for ordered MTP2 random variables: A proof of the Simes conjecture

Annals of Statistics

Volumn 26, Issue 2, 1998, Pages 494-504

  Sarkar, Sanat K ^a  

^a TEMPLE UNIVERSITY   (United States)

Author keywords

P values; Positive dependence; Simes test

Indexed keywords

EID: 0032352436     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (21)

1. DUNNETT, C. W. and SOBEL, M. (1954). A bivariate generalization of Student's t distribution with tables for certain cases. Biometrika 41 153-169.
2. DYKSTRA, R. L. and HEWETT, J. E. (1978). Positive dependence of the roots of a Wishart matrix. Ann. Statist. 6 235-1238.
3. GLAZ, J. and JOHNSON, B. M. (1984). Probability inequalities for multivariate distributions with dependence structures. J. Amer. Statist. Assoc. 79 436-440.
4. HOCHBERG, Y. (1988). A sharper Bonferroni procedure for multiple tests of significance. Biometrika 75 800-802.
5. HOCHBERG, Y. and ROM, D. M. (1995). Extensions of multiple testing procedures based on Simes' test. J. Statist. Plann. Inference 48 141-152.
6. HOLM, S. (1979). A simple sequentially rejective multiple test procedure. Scand. J. Statist. 6 65-70.
7. HOMMEL, G. (1988). A stagewise rejective multiple test procedure based on a modified test procedure. Biometrika 75 383-386.
8. HOMMEL, G. (1989). A comparison of two modified Bonferroni procedures. Biometrika 76 624-625.
9. JOHNSON, N. L. and KOTZ, S. (1972). Distributions in Statistics: Continuous Multivariate Distributions. Wiley, New York.
10. KARLIN, S. (1968). Total Positivity. Stanford Univ. Press.
11. KARLIN, S. and RINOTT, Y. (1980a). Classes of orderings of measures and related correlation inequalities I. Multivariate totally positive distributions. J. Multivariate Anal. 10 467-498.
12. KARLIN, S. and RINOTT, Y. (1980b). Classes of orderings of measures and related correlation inequalities II. Multivariate reverse rule distributions. J. Multivariate Anal. 10 499-516.
13. KARLIN, S. and RINOTT, Y. (1981). Total positivity properties of absolute value multinormal variables with applications to confidence interval estimates and related probabilistic inequalities. Ann. Statist. 9 1035-1049.
14. LIU, W. (1996). Multiple tests of a non-heirarchical finite family of hypotheses. J. Roy. Statist. Soc. Ser. B 58 455-461.
15. PERLMAN, M. D. and OLKIN, I. (1980). Unbiasedness of invariant tests for MANOVA and other multivariate problems. Ann. Statist. 8 1326-1341.
16. ROM, D. M. (1990). A sequentially rejective test procedure based on a modified Bonferroni inequality. Biometrika 77 663-665.
17. SAMUEL-CAHN, E. (1996). Is the Simes improved Bonferroni procedure conservative? Biometrika 83 928-933.
18. SARKAR, S. K. and CHANG, C.-K. (1997). The Simes method for multiple hypothesis testing with positively dependent test statistics. J. Amer. Statist. Assoc. 92 1601-1608.
19. 2 random variables. Sankhyā Ser. A 48 119-135.
20. SIMES, R. J. (1986). An improved Bonferroni procedure for multiple tests of significance. Biometrika 73 751-754.
21. TONG, Y. L. (1980). Probability Inequalities in Multivariate Distributions. Academic Press, New York.