False discovery rate-adjusted multiple confidence intervals for selected parameters
False discovery rate-adjusted multiple confidence intervals for selected parameters
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DOI：
10.1198/016214504000001907
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发表时间：
2005-03-01
影响因子：
3.7
通讯作者：
Yekutieli, D
中科院分区：
文献类型：
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作者：
Benjamini, Y;Yekutieli, D
通常在应用研究中，仅为查看数据后选择的参数构建或报告置信区间（CI）。我们表明，这样选择的间隔未能提供假设的覆盖概率。通过将错误发现率（FDR）方法从多次测试推广到选定的多个CI，我们建议将错误覆盖率（FCR）作为选择后区间覆盖率的衡量标准。然后介绍了一个一般的程序，提供FCR控制在任何选择规则下的水平q。该程序为每个选定的参数构建边际CI，但不是边际使用置信水平1 - q，而是将q除以所考虑的参数数量并乘以选定的数量。如果我们进一步使用Benjamini和Hochberg的FDR控制测试程序来选择参数，则新建议的程序提供了与测试程序对偶的CI，并且在独立情况下被证明是最优的。在Benjamini和Yekutieli的正回归依赖性条件下，对单侧检验和CI以及双侧检验的修改控制FCR。一般依赖的结果也给出。最后，利用CI的等价性进行检验，证明了Benjamini和Hochberg的方法提供了方向FDR控制。
Often in applied research, confidence intervals (CIs) are constructed or reported only for parameters selected after viewing the data. We show that such selected intervals fail to provide the assumed coverage probability. By generalizing the false discover), rate (FDR) approach from multiple testing to selected multiple CIs, we suggest the false coverage-statement rate (FCR) as a measure of interval coverage following selection. A general procedure is then introduced, offering FCR control at level q under any selection rule. The procedure constructs a marginal CI for each selected parameter, but instead of the confidence level 1 - q being used marginally, q is divided by the number of parameters considered and multiplied by the number selected. If we further use the FDR controlling testing procedure of Benjamini and Hochberg for selecting the parameters, the newly suggested procedure offers CIs that are dual to the testing procedure and are shown to be optimal in the independent case. Under the positive regression dependency condition of Benjamini and Yekutieli, the FCR is controlled for one-sided tests and CIs, as well as for a modification for two-sided testing. Results for general dependency are also given. Finally, using the equivalence of the CIs to testing, we prove that the procedure of Benjamini and Hochberg offers directional FDR control as conjectured.