2007/06/30 by Zhiyi Chi
Decision Sciences · Mathematics · #Advanced Statistical Process Monitoring #Statistical Methods and Bayesian Inference #Statistical Methods in Clinical Trials #math.ST #msc:62G10 #msc:62G20 #msc:62H15 #stat.TH
paper · pdf · doi:10.1214/07-ejs147
published as Electronic Journal of Statistics 2008, Vol. 2, 368-411 · Published in at http://dx.doi.org/10.1214/07-EJS147 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2008/01/01 · arxiv created 2008/05/21 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Multivariate statistics are often available as well as necessary in hypothesis tests. We study how to use such statistics to control not only false discovery rate (FDR) but also positive FDR (pFDR) with good power. We show that FDR can be controlled through nested regions of multivariate p-values of test statistics. If the distributions of the test statistics are known, then the regions can be constructed explicitly to achieve FDR control with maximum power among procedures satisfying certain conditions. On the other hand, our focus is where the distributions are only partially known. Under certain conditions, a type of nested regions are proposed and shown to attain (p)FDR control with asymptotically maximum power as the pFDR control level approaches its attainable limit. The procedure based on the nested regions is compared with those based on other nested regions that are easier to construct as well as those based on more straightforward combinations of the test statistics.