Abstract

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 CD-plot. Technical proofs, codes and data are provided in the supplementary material.

摘要

拟合优度的经典测试旨在验证假设模型与研究数据的一致性。鉴于它们的推理性质，它们可以被认为是验证性数据分析的关键步骤。然而，在他们的标准公式中，他们不允许探索假设模型如何偏离事实，也不允许对如何改进被拒绝的模型以更好地拟合数据提供任何见解。这项工作的主要目标是建立一个全面的拟合优度框架，该框架自然地集成了建模、估计、推理和图形。建模和估计侧重于一种新的平滑测试公式，该公式很容易扩展到任意分布，无论是连续的还是离散的。CD-情节。技术证明、代码和数据在补充材料中提供。