A note on control of the false discovery proportion
Volume 36 / 2009
Applicationes Mathematicae 36 (2009), 397-418
MSC: 62J15, 62G10.
DOI: 10.4064/am36-4-2
Abstract
We consider the problem of simultaneous testing of a finite number of null hypotheses $H_{i}$, $i=1,\ldots,s$. Starting from the classical paper of Lehmann (1957), it has become a very popular subject of research. In many applications, particularly in molecular biology (see e.g. Dudoit et al. (2003), Pollard et al. (2005)), the number $s$, i.e. the number of tested hypotheses, is large and the popular procedures that control the familywise error rate (FWERM) have small power. Therefore, we are concerned with another error rate measure, called the false discovery proportion (FDP). We prove some theorems about control of the FDP measure. Our results differ from those obtained by Lehmann and Romano (2005).
