We develop two simple measures of uncertainty for a model selection procedure. The first measure is similar in spirit to confidence set in parameter estimation; the second measure is focusing on error in model selection. The proposed methods are simpler, both conceptually and computationally, than the existing measures of uncertainty in model selection. We recognize major differences between model selection and traditional estimation or prediction problems, and propose reasonable frameworks, under which these measures are developed, and their theoretical properties are established. Empirical studies demonstrate performance of the proposed measures, their superiority over the existing methods, and their relevance to real-life applications.

我们为模型选择程序开发了两种简单的不确定性度量。第一种措施在本质上类似于参数估计中设置的置信度。第二个措施是关注模型选择中的错误。所提出的方法在概念上和计算上都比模型选择中现有的不确定性度量更简单。我们认识到模型选择与传统估计或预测问题之间的主要差异，并提出了合理的框架，在这些框架下可以开发这些措施并建立其理论性质。实证研究证明了所提出的措施的性能，它们相对于现有方法的优越性以及与现实应用的相关性。