## 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).