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We will continue the discussion on control family-wise error rate via the maximal statistic. Given hypotheses \(\{ H_{0i} \}_{i=1}^N\) , for each \(H_{0j}\) , we have a statistic \(T_j\) such that for a single hypothesis, we will reject \(H_{0j}\) if \(T_j \ge q_{\alpha }\) where \(q_{\alpha } = \operatorname *{\text{arg min}}_t\mathbb {P}_{H_0}(|T_j|>t) \le \alpha \) .

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False Discovery Rate

  • 章节

  • 发表日期：

    2025年

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  • Junwei Lu

摘要

We will continue the discussion on control family-wise error rate via the maximal statistic. Given hypotheses \(\{ H_{0i} \}_{i=1}^N\) , for each \(H_{0j}\) , we have a statistic \(T_j\) such that for a single hypothesis, we will reject \(H_{0j}\) if \(T_j \ge q_{\alpha }\) where \(q_{\alpha } = \operatorname *{\text{arg min}}_t\mathbb {P}_{H_0}(|T_j|>t) \le \alpha \) .