Some nonasymptotic results on resampling in high dimension, II: Multiple tests
Sylvain Arlot, Gilles Blanchard, and Etienne Roquain
Source: Ann. Statist. Volume 38, Number 1
(2010), 83-99.
Abstract
In the context of correlated multiple tests, we aim to nonasymptotically control the family-wise error rate (FWER) using resampling-type procedures. We observe repeated realizations of a Gaussian random vector in possibly high dimension and with an unknown covariance matrix, and consider the one- and two-sided multiple testing problem for the mean values of its coordinates. We address this problem by using the confidence regions developed in the companion paper [Ann. Statist. (2009), to appear], which lead directly to single-step procedures; these can then be improved using step-down algorithms, following an established general methodology laid down by Romano and Wolf [J. Amer. Statist. Assoc. 100 (2005) 94–108]. This gives rise to several different procedures, whose performances are compared using simulated data.
First Page:
Show
Hide
Keywords: Family-wise error; multiple testing; high-dimensional data; nonasymptotic error control; resampling; resampled quantile
Full-text: Access denied (no subscription
detected)
We're sorry, but we are unable to provide
you with the full text of this article because we are not able to identify
you as a subscriber.
If you have a personal subscription to
this journal, then please login. If you are already logged in, then you
may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aos/1262271610
Digital Object Identifier: doi:10.1214/08-AOS668
Zentralblatt MATH identifier: 1181.62055
Mathematical Reviews number (MathSciNet): MR2589317
References
[1] Arlot, S., Blanchard, G. and Roquain, É. (2010). Some nonasymptotic results on resampling in high dimension, I: Confidence regions. Ann. Statist. 38 51–82.
Mathematical Reviews (MathSciNet): MR2589316
Zentralblatt MATH: 1180.62066
Digital Object Identifier: doi:10.1214/08-AOS667
Project Euclid: euclid.aos/1262271609
[2] Benjamini, Y. and Hochberg, Y. (1995). Controlling the false discovery rate: A practical and powerful approach to multiple testing. J. Roy. Statist. Soc. Ser. B 57 289–300.
Mathematical Reviews (MathSciNet): MR1325392
JSTOR: links.jstor.org
[3] Blanchard, G. and Roquain, É. (2008). Two simple sufficient conditions for FDR control. Electron. J. Stat. 2 963–992.
Mathematical Reviews (MathSciNet): MR2448601
Digital Object Identifier: doi:10.1214/08-EJS180
Project Euclid: euclid.ejs/1224078069
[4] Blanchard, G. and Roquain, É. (2009). Adaptive FDR control under independence and dependence. J. Mach. Learn. Res. To appear.
[5] Darvas, F., Rautiainen, M., Pantazis, D., Baillet, S., Benali, H., Mosher, J., Garnero, L. and Leahy, R. (2005). Investigations of dipole localization accuracy in MEG using the bootstrap. NeuroImage 25 355–368.
[6] Durot, C. and Rozenholc, Y. (2006). An adaptive test for zero mean. Math. Methods Statist. 15 26–60.
Mathematical Reviews (MathSciNet): MR2225429
[7] Fisher, R. A. (1935). The Design of Experiments. Oliver and Boyd, Edinburgh.
[8] Ge, Y., Dudoit, S. and Speed, T. P. (2003). Resampling-based multiple testing for microarray data analysis. Test 12 1–77.
Mathematical Reviews (MathSciNet): MR1993286
Zentralblatt MATH: 1056.62117
Digital Object Identifier: doi:10.1007/BF02595811
[9] Holm, S. (1979). A simple sequentially rejective multiple test procedure. Scand. J. Statist. 6 65–70.
Mathematical Reviews (MathSciNet): MR538597
[10] Jerbi, K., Lachaux, J.-P., N’Diaye, K., Pantazis, D., Leahy, R. M., Garnero, L. and Baillet, S. (2007). Coherent neural representation of hand speed in humans revealed by MEG imaging. PNAS 104 7676–7681.
[11] Pantazis, D., Nichols, T. E., Baillet, S. and Leahy, R. M. (2005). A comparison of random field theory and permutation methods for statistical analysis of MEG data. NeuroImage 25 383–394.
[12] Pacifico, M. P., Genovese, I., Verdinelli, I. and Wasserman, L. (2004). False discovery control for random fields. J. Amer. Statist. Assoc. 99 1002–1014.
Mathematical Reviews (MathSciNet): MR2109490
Zentralblatt MATH: 1055.62105
Digital Object Identifier: doi:10.1198/0162145000001655
[13] Pollard, K. S. and van der Laan, M. J. (2004). Choice of a null distribution in resampling-based multiple testing. J. Statist. Plann. Inference 125 85–100.
Mathematical Reviews (MathSciNet): MR2086890
Zentralblatt MATH: 1074.62009
Digital Object Identifier: doi:10.1016/j.jspi.2003.07.019
[14] Romano, J. P. (1989). Bootstrap and randomization tests of some nonparametric hypotheses. Ann. Statist. 17 141–159.
Mathematical Reviews (MathSciNet): MR981441
Zentralblatt MATH: 0688.62031
Digital Object Identifier: doi:10.1214/aos/1176347007
Project Euclid: euclid.aos/1176347007
[15] Romano, J. P. (1990). On the behavior of randomization tests without a group invariance assumption. J. Amer. Statist. Assoc. 85 686–692.
Mathematical Reviews (MathSciNet): MR1138350
Zentralblatt MATH: 0706.62047
Digital Object Identifier: doi:10.2307/2290003
JSTOR: links.jstor.org
[16] Romano, J. P. and Wolf, M. (2005). Exact and approximate stepdown methods for multiple hypothesis testing. J. Amer. Statist. Assoc. 100 94–108.
Mathematical Reviews (MathSciNet): MR2156821
Zentralblatt MATH: 1117.62416
Digital Object Identifier: doi:10.1198/016214504000000539
[17] Romano, J. P. and Wolf, M. (2007). Control of generalized error rates in multiple testing. Ann. Statist. 35 1378–1408.
Mathematical Reviews (MathSciNet): MR2351090
Zentralblatt MATH: 1127.62063
Digital Object Identifier: doi:10.1214/009053606000001622
Project Euclid: euclid.aos/1188405615
[18] Westfall, P. H. and Young, S. S. (1993). Resampling-Based Multiple Testing: Examples and Methods for P-Value Adjustment. Wiley, New York.
[19] Yekutieli, D. and Benjamini, Y. (1999). Resampling-based false discovery rate controlling multiple test procedures for correlated test statistics. J. Statist. Plann. Inference 82 171–196.
Mathematical Reviews (MathSciNet): MR1736442
Zentralblatt MATH: 1063.62563
Digital Object Identifier: doi:10.1016/S0378-3758(99)00041-5
