There is recent tremendous interest in statistical methods regarding the false discovery rate (FDR). Two classes of literature on this topic exist. In the first, authors have proposed sequential testing procedures that control the false discovery rate. For the second, authors have studied the procedures involving FDR in a univariate mixture model setting. We consider a decision-theoretic approach to the assessment of FDR-based methods. In particular, we attempt to reconcile the current literature on false discovery rate procedures with more classical simultaneous estimation procedures. Formulation of the link will allow us to apply results from decision theory; we can then traverse between the two literatures. In particular, we propose double shrinkage estimators for the location parameter in the multiple testing problem for false discovery rates and provide conditions for obtaining minimaxity. We also describe a double shrinkage estimation procedure for p-values. Simulation studies are used to explore the risk properties of existing statistical methods and the potential gains of shrinkage. We then develop a procedure for calculating double shrinkage estimators from observed data. The procedures are applied to data from a gene expression profiling study in prostate cancer.
Ghosh, Debashis, "Simultaneous estimation procedures and multiple testing: a decision-theoretic framework" (August 2005). The University of Michigan Department of Biostatistics Working Paper Series. Working Paper 54.