论文标题
从模型选择到模型平均：嵌套线性模型的比较
From Model Selection to Model Averaging: A Comparison for Nested Linear Models
论文作者
论文摘要
具有许多候选模型时，模型选择（MS）和模型平均（MA）是两种流行的方法。从理论上讲，Oracle MA的估计风险并不大于Oracle MS的估计风险，因为前者更灵活，但是基本问题是：MA是否提供了{\ IT}对MS的大量改进？最近，一项开创性的作品：彭和杨（2021），在具有线性正交系列扩展的嵌套模型下回答了这个问题。在当前的论文中，我们在线性嵌套回归模型下进一步回答了这个问题。尤其是，在当前论文中允许使用更一般的嵌套框架，异质和自相关的随机错误以及稀疏系数，这在实践中更为常见。此外，我们将MAS与不同的重量集进行了比较。模拟研究支持各种环境中的理论发现。
Model selection (MS) and model averaging (MA) are two popular approaches when having many candidate models. Theoretically, the estimation risk of an oracle MA is not larger than that of an oracle MS because the former one is more flexible, but a foundational issue is: does MA offer a {\it substantial} improvement over MS? Recently, a seminal work: Peng and Yang (2021), has answered this question under nested models with linear orthonormal series expansion. In the current paper, we further reply this question under linear nested regression models. Especially, a more general nested framework, heteroscedastic and autocorrelated random errors, and sparse coefficients are allowed in the current paper, which is more common in practice. In addition, we further compare MAs with different weight sets. Simulation studies support the theoretical findings in a variety of settings.
