I'm searching for literature on the lasso in a GLM setting. I've looked at Elements of statistical learning (Hastie et al 2009) and Statistical learning with sparsity (Hastie et al 2016). Both of these sources have thorough explanations of the lasso in the context of a linear regression model. I'm aware that properties of the lasso in the linear model, such as variable selection, are similar for a GLM, but it would be nice to see a thorough presentation of the lasso for a GLM.

By the way, I'm more interested in the statistical properties of the lasso, than the algorithms for the fitting process.

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    $\begingroup$ Have you seen Park MY, Hastie T (2007a). L1-Regularization Path Algorithm for Generalized Linear Models. Journal of the Royal Statistical Society B, 69, 659–677 web.stanford.edu/~hastie/Papers/… $\endgroup$ – Cabana May 1 '17 at 10:55
  • $\begingroup$ Thank you for the reference. It sure looks interesting. I wasn't aware that it was possible to state the problem using the derivative of the L1-norm, as in equation 6. $\endgroup$ – harisf May 1 '17 at 12:21
  • $\begingroup$ There is also "Statistics for High Dimensional Data" by Buhlmann and van de Geer that go through the pure theory of LASSO (asymptotics and such). $\endgroup$ – Josh May 1 '17 at 13:47

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