论文标题

用于控制大规模t检验的虚假发现率的新程序

A New Procedure for Controlling False Discovery Rate in Large-Scale t-tests

论文作者

Zou, Changliang, Ren, Haojie, Guo, Xu, Li, Runze

论文摘要

本文涉及大型多重测试问题中的错误发现率(FDR)控制。我们首先提出了一个新的数据驱动的测试程序,用于控制一个样本平均问题的大规模t检验中的FDR。当种群对称时,无论测试数量或样本量多少,所提出的程序都可以在有限样本设置中获得精确的FDR控制。与现有的Bootstrap方法进行FDR控制相比,提出的程序在计算上是有效的。我们表明,即使测试统计量并非独立,提出的方法也可以渐近地控制FDR。我们进一步表明,具有简单校正的提议过程与二阶程度的Bootstrap方法一样准确,并且可能比现有的正常校准更有效。我们将提出的程序扩展到两个样本的平均问题。经验结果表明,当真正的替代假设的比例不太低时,同时保持合理良好的检测能力时,所提出的程序比现有程序更好。

This paper is concerned with false discovery rate (FDR) control in large-scale multiple testing problems. We first propose a new data-driven testing procedure for controlling the FDR in large-scale t-tests for one-sample mean problem. The proposed procedure achieves exact FDR control in finite sample settings when the populations are symmetric no matter the number of tests or sample sizes. Comparing with the existing bootstrap method for FDR control, the proposed procedure is computationally efficient. We show that the proposed method can control the FDR asymptotically for asymmetric populations even when the test statistics are not independent. We further show that the proposed procedure with a simple correction is as accurate as the bootstrap method to the second-order degree, and could be much more effective than the existing normal calibration. We extend the proposed procedure to two-sample mean problem. Empirical results show that the proposed procedures have better FDR control than existing ones when the proportion of true alternative hypotheses is not too low, while maintaining reasonably good detection ability.

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