A sharp upper bound for the expected number of false rejections
We consider the class of monotone multiple testing procedures (monotone MTPs). It includes, among others, traditional step-down (Holm type) and step-up (Benjamini–Hochberg type) MTPs, as well as their generalization–step-up-down procedures (Tamhane et al., 1998). Our main result–the All-or-Nothing Theorem–allows us to explicitly calculate, for each MTP in those classes, its per-family error rate–the exact level at which the procedure controls the expected number of false rejections under general and unknown dependence structure of the individual tests. As an illustration, we show that, for any monotone step-down procedure (where the term “step-down” is understood in the most general sense), the ratio of its per-family error rate and its familywise error rate (the exact level at which the procedure controls the probability of one or more false rejections) does not exceed 4 if the denominator is less than 1.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 82 (2012)
Issue (Month): 8 ()
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description|
|Order Information:|| Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Gordon, Alexander Y. & Salzman, Peter, 2008. "Optimality of the Holm procedure among general step-down multiple testing procedures," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1878-1884, September.
- Gordon, Alexander Y., 2007. "Unimprovability of the Bonferroni procedure in the class of general step-up multiple testing procedures," Statistics & Probability Letters, Elsevier, vol. 77(2), pages 117-122, January.
When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:82:y:2012:i:8:p:1507-1514. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Shamier, Wendy)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.