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This paper continues the line of research initiated in Liu et. al. (2016) ondeveloping a novel framework for multiple testing of hypotheses grouped in aone-way classified form using hypothesis-specific local false discovery rates(Lfdr's). It is built on an extension of the standard two-class mixture modelfrom single to multiple groups, defining hypothesis-specific Lfdr as a functionof the conditional Lfdr for the hypothesis given that it is within an importantgroup and the Lfdr for the group itself and involving a new parameter thatmeasures grouping effect. This definition captures the underlying groupstructure for the hypotheses belonging to a group more effectively than thestandard two-class mixture model. Two new Lfdr based methods, possessingmeaningful optimalities, are produced in their oracle forms. One, designed tocontrol false discoveries across the entire collection of hypotheses, isproposed as a powerful alternative to simply pooling all the hypotheses into asingle group and using commonly used Lfdr based method under the standardsingle-group two-class mixture model. The other is proposed as an Lfdr analogof the method of Benjamini and Bogomolov (2014) for selective inference. Itcontrols Lfdr based measure of false discoveries associated with selectinggroups concurrently with controlling the average of within-group falsediscovery proportions across the selected groups. Simulation studies andreal-data application show that our proposed methods are often more powerfulthan their relevant competitors.

Local False Discovery Rate Based Methods for Multiple Testing of One-Way Classified Hypotheses