Biometrika Advance Access originally published online on October 12, 2009
Biometrika 2009 96(4):1012-1018; doi:10.1093/biomet/asp048
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A note on adaptive Bonferroni and Holm procedures under dependence
Department of Mathematical Sciences, New Jersey Institute of Technology, University Heights, New Jersey 07102-1982, U.S.A. wenge.guo{at}gmail.com
Received for publication 1 March 2008. Revision received 1 March 2009.
Hochberg & Benjamini (1990) first presented adaptive procedures for controlling familywise error rate. However, until now, it has not been proved that these procedures control the familywise error rate. We introduce a simplified version of Hochberg & Benjamini’s adaptive Bonferroni and Holm procedures. Assuming a conditional dependence model, we prove that the former procedure controls the familywise error rate in finite samples while the latter controls it approximately.
Key Words: Bonferroni procedure • Conditional dependence • Familywise error rate • Holm procedure • Multiple testing • Step-down procedure
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