联邦多重检验中族系错误率控制下的报告分辨率

中文摘要 AI 辅助

多个机构在族系错误率控制下检验同一组假设，但无法合并各自的数据，因此每个站点仅针对每个假设发布其自身p值的报告。报告的分辨率是指其能取值的数量。我们量化了相对于最强大的集中式程序（即神谕）而言，此类报告所导致的功效损失，其中报告和合并规则均为最优选择。若能从报告中恢复p值，则不会损失功效，因此损失源于压缩而非去中心化。在所述的正则性和功效目标条件下，任何有限分辨率都会损失功效，且最优损失随分辨率的平方倒数衰减：等宽区间可达到此阶数，且任何划分为相同数量单元格的划分都无法改进。在两个站点的Beta分布示例中，对于单一假设，优化的一位报告几乎无损失，但对于两个假设，其功效损失则高出数倍。在显著性水平0.05下，对于两个Beta(1, 2)假设，最优合并的三位等宽报告保留了神谕功效的99.2%。我们给出了在给定报告下的功效最优合并规则，以及仅利用其精确已知的零分布、在假设间任意依赖下均有效的规则。

英文摘要

Several institutions test one family of hypotheses under family-wise error control but cannot pool their data, so each site releases, for each hypothesis, only a report of its own p-value. The report's resolution is the number of values it can take. We quantify the power lost to such reports relative to the most powerful centralized procedure (the oracle), with reports and combining rule chosen optimally. A report from which the p-value can be recovered loses no power, so the loss is due to compression, not decentralization. Under the stated regularity and power-objective conditions, every finite resolution loses power, and the optimal loss decays as the inverse square of the resolution: equal-width intervals attain this order, and no partition into as many cells improves it. In two-site Beta examples, optimized one-bit reports are nearly lossless for a single hypothesis but lose several times as much power for two. At level 0.05 with two Beta(1, 2) hypotheses, optimally combined three-bit equal-width reports retain 99.2% of oracle power. We give the power-optimal combining rule for given reports, and a rule using only their exactly known null distribution, valid under arbitrary dependence across hypotheses.

发表机构

• H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology（乔治亚理工学院 H. 米尔顿·斯图尔特工业与系统工程学校）

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