Exhaustive Goodness of Fit Via Smoothed Inference and Graphics

Classical tests of goodness of fit aim to validate the conformity of a postulated model to the data under study. Given their inferential nature, they can be considered a crucial step in confirmatory data analysis. In their standard formulation, however, they do not allow exploring how the hypothesized model deviates from the truth nor do they provide any insight into how the rejected model could be improved to better fit the data. The main goal of this work is to establish a comprehensive framework for goodness of fit which naturally integrates modeling, estimation, inference and graphics. Modeling and estimation focus on a novel formulation of smooth tests that easily extends to arbitrary distributions, either continuous or discrete. Inference and adequate post-selection adjustments are performed via a specially designed smoothed bootstrap and the results are summarized via an exhaustive graphical tool called <i>CD-plot</i>. Technical proofs, codes and data are provided in the supplementary material.

经典拟合优度检验旨在验证所假定模型与研究中数据的契合程度。鉴于其具备推断属性，该类检验可被视为验证性数据分析中的关键环节。然而在标准设定下，这类检验既无法探究假设模型与真实情况的偏离方式，也无法为如何改进被拒绝的模型以更好适配数据提供任何启示。本研究的核心目标是构建一套完整的拟合优度检验框架，该框架可自然整合建模、估计、推断与可视化四大模块。建模与估计环节聚焦于一种全新的平滑检验形式，该形式可轻松拓展至任意连续或离散分布场景。推断环节与恰当的选择后校正可通过专门设计的平滑自助法完成，最终结果则通过一款名为CD-plot的详尽可视化工具进行汇总展示。补充材料中提供了技术证明、代码与相关数据集。