Exhaustive Goodness of Fit Via Smoothed Inference and Graphics

Sara Algeri, Xiangyu Zhang

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)378-389
Number of pages12
JournalJournal of Computational and Graphical Statistics
Issue number2
StatePublished - 2022

Bibliographical note

Publisher Copyright:
© 2021 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.


  • Goodness-of-fit
  • Graphical inference
  • Smooth tests
  • Smoothed bootstrap


Dive into the research topics of 'Exhaustive Goodness of Fit Via Smoothed Inference and Graphics'. Together they form a unique fingerprint.

Cite this