On stepdown control of the false discovery proportion
| dc.creator | Romano, Joseph P. | |
| dc.creator | Shaikh, Azeem M. | |
| dc.date | 2006-10-27 | |
| dc.date.accessioned | 2026-07-07T08:08:17Z | |
| dc.date.available | 2026-07-07T08:08:17Z | |
| dc.description | Consider the problem of testing multiple null hypotheses. A classical approach to dealing with the multiplicity problem is to restrict attention to procedures that control the familywise error rate ($FWER$), the probability of even one false rejection. However, if $s$ is large, control of the $FWER$ is so stringent that the ability of a procedure which controls the $FWER$ to detect false null hypotheses is limited. Consequently, it is desirable to consider other measures of error control. We will consider methods based on control of the false discovery proportion ($FDP$) defined by the number of false rejections divided by the total number of rejections (defined to be 0 if there are no rejections). The false discovery rate proposed by Benjamini and Hochberg (1995) controls $E(FDP)$. Here, we construct methods such that, for any $γ$ and $α$, $P\{FDP>γ\}\le α$. Based on $p$-values of individual tests, we consider stepdown procedures that control the $FDP$, without imposing dependence assumptions on the joint distribution of the $p$-values. A greatly improved version of a method given in Lehmann and Romano \citer10 is derived and generalized to provide a means by which any sequence of nondecreasing constants can be rescaled to ensure control of the $FDP$. We also provide a stepdown procedure that controls the $FDR$ under a dependence assumption. | |
| dc.description | Published at http://dx.doi.org/10.1214/074921706000000383 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/math/0610843 | |
| dc.identifier | http://arxiv.org/abs/math/0610843 | |
| dc.identifier | IMS Lecture Notes--Monograph Series 2006, Vol. 49, 33-50 | |
| dc.identifier | doi:10.1214/074921706000000383 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/131214 | |
| dc.subject | Statistics Theory | |
| dc.subject | 62J15 (Primary) | |
| dc.title | On stepdown control of the false discovery proportion | |
| dc.type | text |