Competition-based approach to controlling the false discovery rate (FDR) recently rose to prominence when, generalizing it to sequential hypothesis testing, Barber and Cand\`es used it as part of their knockoff-filter. Control of the FDR implies that the, arguably more important, false discovery proportion is only controlled in an average sense. We present TDC-SB and TDC-UB that provide upper prediction bounds on the FDP in the list of discoveries generated when controlling the FDR using competition. Using simulated and real data we show that, overall, our new procedures offer significantly tighter upper bounds than ones obtained using the recently published approach of Katsevich and Ramdas, even when the latter is further improved using the interpolation concept of Goeman et al.

翻译：基于竞争的虚假发现率（FDR）控制方法近期备受关注，Barber与Candès将其推广至序贯假设检验后，作为其"knockoff-filter"（仿变量滤波器）的核心组件。FDR控制仅能保证虚假发现比例（FDP）在平均意义上得到控制，而这一指标实则更为关键。我们提出TDC-SB与TDC-UB两种方法，可在通过竞争机制控制FDR时，为生成的发现列表中的FDP提供上界预测。模拟与实证数据表明，与Katsevich及Ramdas近期提出的方法相比（即便通过Goeman等人的插值概念对其进一步优化），我们的新方法整体上能提供显著更紧密的上界。