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The Simes Method for Multiple Hypothesis Testing with Positively Dependent Test Statistics
Abstract
The Simes method for testing intersection of more than two hypotheses is known to control the probability of type I error only when the underlying test statistics are independent. Although this method is more powerful than the classical Bonferroni method, it is not known whether it is conservative when the test statistics are dependent. This article proves that for multivariate distributions exhibiting a type of positive dependence that arise in many multiple-hypothesis testing situations, the Simes method indeed controls the probability of type I error. This extends some results established very recently in the special case of two hypotheses.
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Citations
Cites
An improved Bonferroni procedure for multiple tests of significance
SIMES, R. J. (1986) · Biometrika · doi:10.1093/biomet/73.3.751 · Cited by 2,396
Multiple Comparison Procedures
Hochberg, Y., & Tamhane, A. C. (1987) · Wiley Series in Probability and Statistics · doi:10.1002/9780470316672 · Cited by 2,389
Cited by
The control of the false discovery rate in multiple testing under dependency
Benjamini, Y., & Yekutieli, D. (2001) · The Annals of Statistics · doi:10.1214/aos/1013699998 · Cited by 10,490
Microbial co-occurrence relationships in the human microbiome
Faust, K., Sathirapongsasuti, J. F., Izard, J., Segata, N., Gevers, D., Raes, J., & Huttenhower, C. (2012) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1002606 · Cited by 1,527
Bretz, F., Hothorn, T., & Westfall, P. (2016) · doi:10.1201/9781420010909 · Cited by 1,233
Overview of Friedman’s test and post-hoc analysis
Pereira, D. G., Afonso, A., & Medeiros, F. M. (2015) · Communications in Statistics - Simulation and Computation · doi:10.1080/03610918.2014.931971 · Cited by 585
Generalizations of the familywise error rate
Lehmann, E. L., & Romano, J. P. (2005) · The Annals of Statistics · doi:10.1214/009053605000000084 · Cited by 320
“In particular, Sarkar and Chang [11] and Sarkar [10] have shown that the Simes inequality holds for the family of distributions which is characterized by the multivariate positive of order 2 condition, as well as some other important distributions.”
Background
Metadata
- Authors
- Sarkar, S. K., & Chang, C.-K.
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 1997-12
- Volume
- 92
- Issue
- 440
- Pages
- 1601-1608
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W2071152671
- Cited by
- 336
- References
- 2
- FWCI
- 4.27
- Type
- journal article
- Language
- en
- Open access
- closed
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- Sarkar, S. K., & Chang, C.-K. (1997). The Simes Method for Multiple Hypothesis Testing with Positively Dependent Test Statistics. Journal of the American Statistical Association. https://doi.org/10.1080/01621459.1997.10473682
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