Generalised Linear Models

By N. H. Bingham, J. Fry. 2010

335 citations recorded by the source corpus.

In previous chapters, we have studied the model $$y = A\beta + \epsilon, $$ where the mean Ey = Aβ depends linearly on the parameters β, the errors are normal (Gaussian), and the errors are additive. We have also seen (Chapter 7) that in some situations, a transformation of the problem may help to correct some departure from our standard model assumptions. For example, in §7.3 on variance-stabilising transformations, we transformed our data from y to some function g(y), to make the variance constant (at least approximately). We did not there address the effect on the error structure of so doing. Of course, \(g(y) = g(A\beta + \epsilon )\) as above will not have an additive Gaussian error structure any more, even approximately, in general.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/f560363b3119a04948a82a67af3623106cb618e6

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In Applied Mathematics

1. Shai Shalev-Shwartz
2. Kfir Yehuda Levy
3. Elad Hazan

Citations in the corpus

• Least angle and ℓ1 penalized regression: A review (2008, background): “This is the marginality principle in linear models (McCullagh and Nelder, 1989) and heredity principle in design of experiments (Hamada and Wu, 1992).”
• Beyond Convexity: Stochastic Quasi-Convex Optimization (2015, methodology): “In the noisy GLM setup (see [14, 7]), we may draw i.”