“A Closer Look at the Deviance” by T. Hastie

Comment on... Maximum Likelihood Estimation Linear Models Statistics

A nice review of properties of Deviance for one parameter exponential families.

Valerio Gherardi https://vgherard.github.io

(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:

Hastie, Trevor. 1987. “A Closer Look at the Deviance.” The American Statistician 41 (1): 16–20. https://doi.org/10.1080/00031305.1987.10475434.



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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

  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}