Classes of Multiple Decision Functions Strongly Controlling FWER and FDR

TL;DR

This paper introduces two broad classes of multiple decision functions that strongly control FWER and FDR, enabling optimal testing strategies in high-dimensional data analysis like microarrays.

Contribution

It proposes new classes of decision functions that guarantee error rate control and can be optimized for specific criteria in multiple testing scenarios.

Findings

Two classes of decision functions controlling FWER and FDR.

Potential to find optimal decision functions within these classes.

Applicable to high-dimensional data analysis such as microarray studies.

Abstract

This paper provides two general classes of multiple decision functions where each member of the first class strongly controls the family-wise error rate (FWER), while each member of the second class strongly controls the false discovery rate (FDR). These classes offer the possibility that an optimal multiple decision function with respect to a pre-specified criterion, such as the missed discovery rate (MDR), could be found within these classes. Such multiple decision functions can be utilized in multiple testing, specifically, but not limited to, the analysis of high-dimensional microarray data sets.