Model Selection by Testing for the Presence of Small-Area Effects, and Application to Area-Level Data
Model Selection by Testing for the Presence of Small-Area Effects, and Application to Area-Level Data
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DOI：
10.1198/jasa.2011.tm10036
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发表时间：
2011-03-01
影响因子：
3.7
通讯作者：
Mandal, Abhyuday
中科院分区：
文献类型：
--
作者：
Datta, Gauri S.;Hall, Peter;Mandal, Abhyuday
小区域推理中使用的模型通常涉及不可观察的随机效应。虽然这可以显着提高模型的适应性和灵活性，但它也增加了点估计器和区间估计器的可变性。如果我们能够测试随机效应的存在，并且如果测试表明它们不太可能存在，那么我们可以说不需要将它们纳入模型中，从而可以显着提高方法的精度。在本文中，我们建议采用这种类型的方法。我们开发了简单的引导方法来测试随机效应的存在，其适用范围远远超出了自然指数族的传统背景。如果不拒绝影响不存在的零假设，那么我们的通用方法立即使我们能够访问未知模型参数的估计器和小区域均值的估计器。例如，这样的估计器可以更加有效，因为当模型包含随机效应时，它们的收敛速度比对应的估计器快得多。如果零假设被拒绝，那么下一步要么使模型更加复杂（我们的方法非常普遍），要么转向现有的随机效应模型。本文有在线补充材料。
The models used in small-area inference often involve unobservable random effects. While this can significantly improve the adaptivity and flexibility of a model, it also increases the variability of both point and interval estimators. If we could test for the existence of the random effects, and if the test were to show that they were unlikely to be present, then we would arguably not need to incorporate them into the model, and thus could significantly improve the precision of the methodology. In this article we suggest an approach of this type. We develop simple bootstrap methods for testing for the presence of random effects, applicable well beyond the conventional context of the natural exponential family. If the null hypothesis that the effects are not present is not rejected then our general methodology immediately gives us access to estimators of unknown model parameters and estimators of small-area means. Such estimators can be substantially more effective, for example, because they enjoy much faster convergence rates than their counterparts when the model includes random effects. If the null hypothesis is rejected then the next step is either to make the model more elaborate (our methodology is available quite generally) or to turn to existing random effects models. This article has supplementary material online.