Asymptotic properties of false discovery rate controlling procedures under independence

Electronic Journal of Statistics

Volumn 2, Issue , 2008, Pages 1065-1110

  Neuvial, Pierre ^a,b,c,d  

^a UNIVERSITÉ PARIS DESCARTES   (France)

^b INSERM U900   (France)

^c PSL RESEARCH UNIVERSITY   (France)

^d INSTITUT CURIE   (France)

Author keywords

Benjamini Hochberg procedure; FDP; FDR; Multiple hypothesis testing

Indexed keywords

EID: 73949108401     PISSN: 19357524     EISSN: None     Source Type: Journal    
DOI: 10.1214/08-EJS207     Document Type: Article

References (28)

1. Benjamini, Y. And Hochberg, Y. (1995). Controlling the false discovery rate: A practical and powerful approach to multiple testing. J. R. Stat. Soc. Ser. B Stat. Methodol. 57, 1, 289-300.
2. Benjamini, Y., Krieger, A. M., and Yekutieli, D. (2006). Adaptive linear step-up procedures that control the false discovery rate. Biometrika 93, 3, 491-507.
3. Benjamini, Y. And Yekutieli, D. (2001). The control of the false discovery rate in multiple testing under dependency. Ann. Statist. 29, 4, 1165-1188.
4. Blanchard, G. And Roquain, E. (2008). Adaptive FDR control under independence and dependence. ArXiv preprint math.ST/0707.0536.
5. Chi, Z. (2007). On the performance of FDR control: constraints and a partial solution. Ann. Statist. 35, 4, 1409-1431.
6. Donsker, M. D. (1951). An invariance principle for certain probability limit theorems. Mem. Amer. Math. Soc. 6, 12.
7. Finner, H., Dickhaus, T., and Roters, M. (2008). On the false discovery rate and an asymptotically optimal rejection curve. Ann. Statist. (to appear).
8. Finner, H. And Roters, M. (2001). On the false discovery rate and expected type I errors. Biom. J. 43, 8, 985-1005.
9. Finner, H. And Roters, M. (2002). Multiple hypotheses testing and expected number of type I errors. Ann. Statist. 30, 1, 220-238.
10. Genovese, C. And Wasserman, L. (2002). Operating characteristics and extensions of the false discovery rate. J. R. Stat. Soc. Ser. B Stat. Methodol. 64, 3, 499-517.
11. Genovese, C. And Wasserman, L. (2004). A stochastic process approach to false discovery control. Ann. Statist. 32, 3, 1035-1061.
12. Genovese, C. And Wasserman, L. (2006). Exceedance control of the false discovery proportion. J. Amer. Statist. Assoc. 101, 476, 1408-1417.
13. Lehmann, E. L. And Romano, J. P. (2005). Generalizations of the family wise error rate. Ann. Statist 33, 3, 1138-1154.
14. Neuvial, P. (2008). Intrinsic bounds and false discovery rate control in multiple testing problems. In revision for J. Mach. Learn. Res.
15. Perone Pacifico, M., Genovese, C., Verdinelli, I., and Wasserman, L. (2004). False discovery control for random fields. J. Amer. Statist. Assoc. 99, 468, 1002-1014.
16. Romano, J. P. And Shaikh, A. M. (2006a). On stepdown control of the false discovery proportion. In Optimality: The Second Erich L. Lehmann Symposium, J. Rojo, Ed. Vol. 33. Institute of Mathematical Statistics, Beachwood, Ohio, USA.
17. Romano, J. P. And Shaikh, A. M. (2006b). Step-up procedures for control of generalizations of the family-wise error rate. Ann. Statist. 34, 4, 1850-1873.
18. Romano, J. P. And Wolf, M. (2007). Control of generalized error rates in multiple testing. Ann. Statist. 35, 4, 1378-1408.
19. Sarkar, S. K. (2002). Some results on false discovery rate in stepwise multiple testing procedures. Ann. Statist. 30, 1, 239-257.
20. Simes, R. J. (1986). An improved Bonferroni procedure for multiple tests of significance. Biometrika 73, 3, 751-754.
21. Storey, J. D. (2002). A direct approach to false discovery rates. J. R. Stat. Soc. Ser. B Stat. Methodol. 64, 3, 479-498.
22. Storey, J. D. (2003). The positive false discovery rate: a bayesian interpretation and the q-value. Ann. Statist. 31, 6, 2013-2035.
23. Storey, J. D., Taylor, J. E., and Siegmund, D. (2004). Strong control, conservative point estimation and simultaneous conservative consistency of false discovery rates: a unified approach. J. R. Stat. Soc. Ser. B Stat. Methodol. 66, 1, 187-205.
24. Storey, J. D. And Tibshirani, R. (2003). SAM thresholding and false discovery rates for detecting differential gene expression in DNA microarrays. In The Analysis of Gene Expression Data: Methods and Software. Springer, New York, 272-290.
25. Sun, W. And Cai, T. T. (2007). Oracle and adaptive compound decision rules for false discovery rate control. J. Amer. Statist. Assoc. 102, 479, 901-912.
26. van der Laan, M. J., Dudoit, S., and Pollard, K. S. (2004). Augmentation procedures for control of the generalized family-wise error rate and tail probabilities for the proportion of false positives. Stat. Appl. Genet. Mol. Biol. 3, Art. 15, 27 pp.
27. van der Vaart, A. W. (1998). Asymptotic Statistics. Cambridge University Press.
28. Wu, W. B. (2008). On false discovery control under dependence. Ann.Statist. 36, 1, 364-380.