Generalized linear model: Difference between revisions

Revision as of 16:31, 22 February 2025

Revision as of 16:41, 22 February 2025

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For scalar <math>\mathbf{y}</math> and <math>\boldsymbol\theta</math>, this reduces to

:<math>\operatorname{Var}(y) = A''(\theta) d(\tau). \,\!</math>

For non-negative response <math>y</math>, assumption-free GLM framework has been developed.<ref>{{Cite journal |last=Babkin |first=Andrey |title=Assumption-lean regression for non-negative response via variational representation |url=https://www.tandfonline.com/doi/full/10.1080/10618600.2025.2459277 |journal=Journal of Computational and Graphical Statistics |volume=0 |issue=ja |pages=1–13 |doi=10.1080/10618600.2025.2459277 |issn=1061-8600}}</ref> Under this framework, the conditional distribution is no longer limited by exponential families.

=== Linear predictor ===