Stepup procedures controlling generalized FWER and generalized FDR
| dc.creator | Sarkar, Sanat K. | |
| dc.date | 2008-03-20 | |
| dc.date.accessioned | 2026-07-07T12:17:46Z | |
| dc.date.available | 2026-07-07T12:17:46Z | |
| dc.description | In many applications of multiple hypothesis testing where more than one false rejection can be tolerated, procedures controlling error rates measuring at least $k$ false rejections, instead of at least one, for some fixed $k\ge 1$ can potentially increase the ability of a procedure to detect false null hypotheses. The $k$-FWER, a generalized version of the usual familywise error rate (FWER), is such an error rate that has recently been introduced in the literature and procedures controlling it have been proposed. A further generalization of a result on the $k$-FWER is provided in this article. In addition, an alternative and less conservative notion of error rate, the $k$-FDR, is introduced in the same spirit as the $k$-FWER by generalizing the usual false discovery rate (FDR). A $k$-FWER procedure is constructed given any set of increasing constants by utilizing the $k$th order joint null distributions of the $p$-values without assuming any specific form of dependence among all the $p$-values. Procedures controlling the $k$-FDR are also developed by using the $k$th order joint null distributions of the $p$-values, first assuming that the sets of null and nonnull $p$-values are mutually independent or they are jointly positively dependent in the sense of being multivariate totally positive of order two (MTP$_2$) and then discarding that assumption about the overall dependence among the $p$-values. | |
| dc.description | Published in at http://dx.doi.org/10.1214/009053607000000398 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/0803.2934 | |
| dc.identifier | http://arxiv.org/abs/0803.2934 | |
| dc.identifier | Annals of Statistics 2007, Vol. 35, No. 6, 2405-2420 | |
| dc.identifier | doi:10.1214/009053607000000398 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/212188 | |
| dc.subject | Statistics Theory | |
| dc.subject | 62J15, 62H15 (Primary) 62H99 (Secondary) | |
| dc.title | Stepup procedures controlling generalized FWER and generalized FDR | |
| dc.type | text |