Exhaustive Goodness of Fit Via Smoothed Inference and Graphics
本文建立了一个整合建模、估计、推断和图形的拟合优度框架，通过平滑检验和CD-plot图形工具，帮助研究者探索模型偏差并改进模型。
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.