On Various Confidence Intervals Post-Model-Selection
On Various Confidence Intervals Post-Model-Selection
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DOI：
10.1214/14-sts507
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发表时间：
2015-05-01
影响因子：
5.7
通讯作者：
Ewald, Karl
中科院分区：
文献类型：
--
作者：
Leeb, Hannes;Poetscher, Benedikt M.;Ewald, Karl
我们比较了Berk等人最近研究的模型选择后的几个置信区间。Statist. 41(2013) 802-837]，其中目标不是覆盖真实参数，而是覆盖取决于所选模型的某个非标准兴趣量。特别是，我们将该参考文献中提出的posii区间与“朴素”置信区间进行了比较，“朴素”置信区间的构造就好像所选模型是正确的并且是先验的固定的（因此忽略了模型选择的存在）。总的来说，我们发现所有这些区间的实际覆盖概率与期望的名义覆盖概率只有适度的偏离。这一发现与现有文献中的几篇论文形成鲜明对比，这些论文的目标是覆盖真实参数。
We compare several confidence intervals after model selection in the setting recently studied by Berk et al. [Ann. Statist. 41 (2013) 802-837], where the goal is to cover not the true parameter but a certain nonstandard quantity of interest that depends on the selected model. In particular, we compare the PoSI-intervals that are proposed in that reference with the "naive" confidence interval, which is constructed as if the selected model were correct and fixed a priori (thus ignoring the presence of model selection). Overall, we find that the actual coverage probabilities of all these intervals deviate only moderately from the desired nominal coverage probability. This finding is in stark contrast to several papers in the existing literature, where the goal is to cover the true parameter.