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Controlling the false discovery rate (FDR) is a powerful approach to multipletesting. In many applications, the tested hypotheses have an inherenthierarchical structure. In this paper, we focus on the fixed sequence structurewhere the testing order of the hypotheses has been strictly specified inadvance. We are motivated to study such a structure, since it is the most basicof hierarchical structures, yet it is often seen in real applications such asstatistical process control and streaming data analysis. We first consider aconventional fixed sequence method that stops testing once an acceptanceoccurs, and develop such a method controlling the FDR under both arbitrary andnegative dependencies. The method under arbitrary dependency is shown to beunimprovable without losing control of the FDR and unlike existing FDR methods;it cannot be improved even by restricting to the usual positive regressiondependence on subset (PRDS) condition. To account for any potential mistakes inthe ordering of the tests, we extend the conventional fixed sequence method toone that allows more but a given number of acceptances. Simulation studies showthat the proposed procedures can be powerful alternatives to existing FDRcontrolling procedures. The proposed procedures are illustrated through a realdata set from a microarray experiment.

The Control of the False Discovery Rate in Fixed Sequence Multiple Testing