This paper continues the line of research initiated in Liu et. al. (2016) on developing a novel framework for multiple testing of hypotheses grouped in a one-way classified form using hypothesis-specific local false discovery rates (Lfdr's). It is built on an extension of the standard two-class mixture model from single to multiple groups, defining hypothesis-specific Lfdr as a function of the conditional Lfdr for the hypothesis given that it is within an important group and the Lfdr for the group itself and involving a new parameter that measures grouping effect. This definition captures the underlying group structure for the hypotheses belonging to a group more effectively than the standard two-class mixture model. Two new Lfdr based methods, possessing meaningful optimalities, are produced in their oracle forms. One, designed to control false discoveries across the entire collection of hypotheses, is proposed as a powerful alternative to simply pooling all the hypotheses into a single group and using commonly used Lfdr based method under the standard single-group two-class mixture model. The other is proposed as an Lfdr analog of the method of Benjamini and Bogomolov (2014) for selective inference. It controls Lfdr based measure of false discoveries associated with selecting groups concurrently with controlling the average of within-group false discovery proportions across the selected groups. Simulation studies and real-data application show that our proposed methods are often more powerful than their relevant competitors.
翻译:本文继续了刘等人(Liu et al. al.)(2016年)启动的关于开发一个新框架以利用当地虚假发现率(Lfdr's),对单向分类的假设进行多重测试的新式框架的研究方针。它建立在标准双级混合模型从单一组向多个组扩展标准双级混合模型的基础上,将特定假设Lfdr定义为有条件Lfdr对假设的函数,因为它属于一个重要组和集团本身的Lfdr,并包含一个测量组合效应的新参数。这一定义捕捉了属于一个集团的假设的基组结构,比标准的双级混合模型更有效。两种新的基于Lfdr的基于Lfdr的新方法,具有有意义的最佳性,以它们的形式从一个组到多个组;其中一项是旨在控制整个假设集的有条件Lfdr的Lfdr, 作为一种强有力的替代方法,仅将所有假设都集中到一个组中,使用通常使用的Lfdurdur制方法衡量组合的效果。另一个是作为Lfdr的基调标准单类混合物模型中较强的基数类模型的基数级模型的基数,在Benjalifr 和Benemal-r imal-laveill rodrodrodrodrodrodro) 中,在选择一个相关的精制的测测测测测测的平平平级的平级的比比制方法中选择的基组。