Cullan Michael, Lidgard Scott, Sterner Beckett
School of Mathematics and Statistical Sciences, Arizona State University, Phoenix, AZ, USA.
Field Museum of Natural History, Chicago, IL, USA.
J Appl Stat. 2019 Dec 18;47(13-15):2565-2581. doi: 10.1080/02664763.2019.1701636. eCollection 2020.
The Akaike Information Criterion (AIC) and related information criteria are powerful and increasingly popular tools for comparing multiple, non-nested models without the specification of a null model. However, existing procedures for information-theoretic model selection do not provide explicit and uniform control over error rates for the choice between models, a key feature of classical hypothesis testing. We show how to extend notions of Type-I and Type-II error to more than two models without requiring a null. We then present the Error Control for Information Criteria (ECIC) method, a bootstrap approach to controlling Type-I error using Difference of Goodness of Fit (DGOF) distributions. We apply ECIC to empirical and simulated data in time series and regression contexts to illustrate its value for parametric Neyman-Pearson classification. An R package implementing the bootstrap method is publicly available.
赤池信息准则（AIC）及相关信息准则是功能强大且日益流行的工具，用于比较多个非嵌套模型，而无需指定零模型。然而，现有的信息论模型选择程序并未像经典假设检验的关键特征那样，对模型间选择的错误率提供明确且统一的控制。我们展示了如何在无需零模型的情况下，将I型和II型错误的概念扩展到两个以上的模型。然后，我们提出了信息准则的错误控制（ECIC）方法，这是一种使用拟合优度差异（DGOF）分布来控制I型错误的自助法。我们将ECIC应用于时间序列和回归背景下的实证数据和模拟数据，以说明其在参数奈曼-皮尔逊分类中的价值。一个实现该自助法的R包已公开发布。
