In this work, the distributional properties of the goodness-of-fit term in likelihood-based information criteria are explored. These properties are then leveraged to construct a novel goodness-of-fit test for normal linear regression models that relies on a non-parametric bootstrap. Several simulation studies are performed to investigate the properties and efficacy of the developed procedure, with these studies demonstrating that the bootstrap test offers distinct advantages as compared to other methods of assessing the goodness-of-fit of a normal linear regression model.

翻译：本研究探讨了基于似然信息准则中拟合优度项的分布特性。利用这些特性，构建了一种依赖于非参数Bootstrap的正态线性回归模型拟合优度检验新方法。通过多项模拟研究评估所提方法的性质与有效性，结果表明：与其他正态线性回归模型拟合优度评估方法相比，该Bootstrap检验具有显著优势。