Selection Adjusted Confidence Intervals With More Power to Determine the Sign
Selection Adjusted Confidence Intervals With More Power to Determine the Sign
复制标题
选择具有更强确定符号能力的调整置信区间
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
Y. Benjamini
中科院分区：
文献类型：
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作者：
A. Weinstein;William Fithian;Y. Benjamini
在许多当前的大规模问题中，置信区间（CI）仅用于其估计器所表明的大参数，忽略了较小的参数。这样的选择性推论给通常的边缘CI带来了一个问题，即不再提供适当的覆盖范围，即使在所选参数上平均也不提供。我们通过开发三种方法来解决此问题，以构建对称单峰分布的位置参数的简短和有效的CI，同时根据其估计器的条件大于某些恒定阈值。在这些方法中的两种中，需要进一步提供CI来提供早期符号确定，即避免在相对较小的估计值值中包含两个符号的参数。有条件的准惯性CI之一，在保护效果的同时，在长度和符号确定之间提供了良好的平衡。 CI不是对称的，延伸到远离它的0，也不是恒定的形状。但是，当估计器远离阈值时，提出的CI趋向于通常的边缘。尽管具有复杂性，但它是由封闭形式表达式指定的，直至一组常数，它们都是单个变量方程的解决方案。当使用多个测试过程来控制错误的发现率或其他错误率时，选择的阈值可能取决于数据。我们表明，在数据依赖性阈值上进行上述CI仍然为许多广泛使用的测试程序提供错误的覆盖率（FCR）。由于这些原因，选择此方式选择的参数的条件CI是可用的一般FCR调整间隔的有吸引力的替代方法。我们证明了该方法在分析激素变化与大脑活动变化之间的大约14,000个相关性，以应对受试者暴露于压力大的电影剪辑。本文的补充材料可在线获得。
In many current large-scale problems, confidence intervals (CIs) are constructed only for the parameters that are large, as indicated by their estimators, ignoring the smaller parameters. Such selective inference poses a problem to the usual marginal CIs that no longer offer the right level of coverage, not even on the average over the selected parameters. We address this problem by developing three methods to construct short and valid CIs for the location parameter of a symmetric unimodal distribution, while conditioning on its estimator being larger than some constant threshold. In two of these methods, the CI is further required to offer early sign determination, that is, to avoid including parameters of both signs for relatively small values of the estimator. One of the two, the Conditional Quasi-Conventional CI, offers a good balance between length and sign determination while protecting from the effect of selection. The CI is not symmetric, extending more toward 0 than away from it, nor is it of constant shape. However, when the estimator is far away from the threshold, the proposed CI tends to the usual marginal one. In spite of its complexity, it is specified by closed form expressions, up to a small set of constants that are each the solution of a single variable equation. When multiple testing procedures are used to control the false discovery rate or other error rates, the resulting threshold for selecting may be data dependent. We show that conditioning the above CIs on the data-dependent threshold still offers false coverage-statement rate (FCR) for many widely used testing procedures. For these reasons, the conditional CIs for the parameters selected this way are an attractive alternative to the available general FCR adjusted intervals. We demonstrate the use of the method in the analysis of some 14,000 correlations between hormone change and brain activity change in response to the subjects being exposed to stressful movie clips. Supplementary materials for this article are available online.
影响因子：
2.1
作者：
Zhong, Hua;Prentice, Ross L.
通讯作者：
Prentice, Ross L.