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

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

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Maximum Likelihood Estimation
Linear Models
Statistics
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Published

March 7, 2024

(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:

References

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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BibTeX citation:
@online{gherardi2024,
  author = {Gherardi, Valerio},
  title = {“{A} {Closer} {Look} at the {Deviance}” by {T.} {Hastie}},
  date = {2024-03-07},
  url = {https://vgherard.github.io/posts/2024-03-07-a-closer-look-at-the-deviance-by-t-hastie/a-closer-look-at-the-deviance-by-t-hastie.html},
  langid = {en}
}
For attribution, please cite this work as:
Gherardi, Valerio. 2024. ‘A Closer Look at the Deviance’ by T. Hastie.” March 7, 2024. https://vgherard.github.io/posts/2024-03-07-a-closer-look-at-the-deviance-by-t-hastie/a-closer-look-at-the-deviance-by-t-hastie.html.