On the large-sample minimal coverage probability of confidence intervals after model selection
On the large-sample minimal coverage probability of confidence intervals after model selection
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DOI：
10.1198/016214505000001140
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发表时间：
2006-06-01
影响因子：
3.7
通讯作者：
Leeb, Hannes
中科院分区：
文献类型：
--
作者：
Kabaila, Paul;Leeb, Hannes
我们给出了当基础模型被“保守”(或“过度一致”)模型选择过程选择时，回归参数通常的置信度区间的最小覆盖概率的大样本分析。我们得到了这类区间的大样本极限最小覆盖概率的上界，它适用于包括Akaike信息准则在内的一大类模型选择过程以及各种预测检验过程。这一上限可用作安全措施，以识别实际覆盖概率可能远低于名义水平的情况。我们说明，即使在相当小的样本中，(渐近)上界也可以是统计上有意义的。
We give a large-sample analysis of the minimal coverage probability of the usual confidence intervals for regression parameters when the underlying model is chosen by a "conservative" (or "overconsistent") model selection procedure. We derive an upper bound for the large-sample limit minimal coverage probability of such intervals that applies to a large class of model selection procedures including the Akaike information criterion as well as various pretesting procedures. This upper bound can be used as a safeguard to identify situations where the actual coverage probability can be far below the nominal level. We illustrate that the (asymptotic) upper bound can be statistically meaningful even in rather small samples.