A nice review of properties of Deviance for one parameter exponential families.
(Hastie 1987). This short review provides a compendium of useful results on the deviance defined by \(\text -2 \log \mathcal L +2\log\mathcal L^*\), where \(\mathcal L^*\) denotes the likelihood of a “saturated” model, as explained in the paper. From the paper’s abstract:
Prediction error and Kullback-Leibler distance provide a useful link between least squares and maximum likelihood estimation. This article is a summary of some existing results, with special reference to the deviance function popular in the GLIM literature.
Of particular interest:
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For attribution, please cite this work as
Gherardi (2024, March 7). vgherard: "A Closer Look at the Deviance" by T. Hastie. Retrieved from https://vgherard.github.io/posts/2024-03-07-a-closer-look-at-the-deviance-by-t-hastie/
BibTeX citation
@misc{gherardi2024"a,
author = {Gherardi, Valerio},
title = {vgherard: "A Closer Look at the Deviance" by T. Hastie},
url = {https://vgherard.github.io/posts/2024-03-07-a-closer-look-at-the-deviance-by-t-hastie/},
year = {2024}
}