Abstract
We introduce two new tools to assess the validity of statistical distributions. Both the simple and composite null hypothesis contexts are considered. These tools are based on components derived from a new statistical quantity, the comparison curve, which can provide a detailed appraisal of validity. The first tool is a graphical representation of these components on a bar plot (B-plot) accompagnied with related local acceptance regions. These allow getting some ideas and building some confidence about where and to which extent the data contradict the model. The knowledge such gained could also suggest an existing goodness-of-fit test to supplement this assessment with a control of the type I error. Otherwise, a new test may be preferable and the second tool is is the combination of these components to produce a powerful -type goodness-of-fit test. Because the number of these components can be large, we introduce new selection rules to decide on their number. In simulations, our new adaptive goodness-of-fit tests are powerwise competitive with the best solutions recommended. Practical examples show how to use these tools to derive principled information regarding if and possibly where the model departs from the data.
Acknowledgments
The authors would like to thank the AE for his/her handling of the manuscript and some useful suggestions. We are also very grateful to an anonymous referee for constructive contributions that greatly improved the readability of the paper. Finally the authors would like to thank Professor Pierre Lafaye de Micheaux for his help with the installation of the codes performing the computations of the paper on the repository site GITHUB.
Citation
Gilles R. Ducharme. Teresa Ledwina. "A new set of tools for goodness-of-fit validation." Electron. J. Statist. 18 (2) 3170 - 3211, 2024. https://doi.org/10.1214/24-EJS2266
Information