In multiple hypotheses testing it has become widely popular to make inference on the true discovery proportion (TDP) of a set $\mathcal{M}$ of null hypotheses. This approach is useful for several application fields, such as neuroimaging and genomics. Several procedures to compute simultaneous lower confidence bounds for the TDP have been suggested in prior literature. Simultaneity allows for post-hoc selection of $\mathcal{M}$. If sets of interest are specified a priori, it is possible to gain power by removing the simultaneity requirement. We present an approach to compute lower confidence bounds for the TDP if the set of null hypotheses is defined a priori. The proposed method determines the bounds using the exact distribution of the number of rejections based on a step-up multiple testing procedure under independence assumptions. We assess robustness properties of our procedure and apply it to real data from the field of functional magnetic resonance imaging.

翻译：在多重假设检验中，基于零假设集合$\mathcal{M}$对真阳性比例进行推断已变得广泛流行。该方法适用于神经影像学和基因组学等多个应用领域。已有文献提出了多种同时计算TDP下置信界的程序。同时性允许事后选择$\mathcal{M}$。若感兴趣集合是事先指定的，则可以通过移除同时性要求来提高统计功效。我们提出了一种方法，在零假设集合事先定义的情况下计算TDP的下置信界。该方法基于独立假设下的逐步向上多重检验程序，利用拒绝次数的精确分布确定置信界。我们评估了该方法的稳健性，并将其应用于功能性磁共振成像领域的真实数据。