Frequentist model average estimators
Frequentist model average estimators
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DOI：
10.1198/016214503000000828
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发表时间：
2003-12-01
影响因子：
3.7
通讯作者：
Claeskens, G
中科院分区：
文献类型：
--
作者：
Hjort, NL;Claeskens, G
模型选择方法在实践中的传统使用是，就好像最终选择的模型已经预先选定一样，而不承认模型选择带来的额外不确定性。这通常意味着低估了可变性和过于乐观的可信区间。我们建立了一个一般的大样本似然工具，它精确地描述了选择后估计量和模型平均估计量的极限分布和风险性质，并显式地考虑了建模偏差。这可以大大降低复杂性，因为可以在只有几个关键量重要的统计原型实验中开发、讨论和比较相互竞争的模型平均方案。特别是，我们提供了贝叶斯模型平均方法的频率观点，并给出了与广义岭估计的联系。我们的工作还导致了新的模型选择标准。并以实际数据应用为例说明了这些方法。
The traditional use of model selection methods in practice is to proceed as if the final selected model had been chosen in advance, without acknowledging the additional uncertainty introduced by model selection. This often means underreporting of variability and too optimistic confidence intervals. We build a general large-sample likelihood apparatus in which limiting distributions and risk properties of estimators post-selection as well as of model average estimators are precisely described, also explicitly taking modeling bias into account. This allows a drastic reduction in complexity, as competing model averaging schemes may be developed, discussed, and compared inside a statistical prototype experiment where only a few crucial quantities matter. In particular, we offer a frequentist view on Bayesian model averaging methods and give a link to generalized ridge estimators. Our work also leads to new model selection criteria. The methods are illustrated with real data applications.