Gaussian approximations hold for high-dimensional GLMs up to d = o(n^{2/5}) for convex sets while bootstrap approximations stay valid further, including in sparse exponential high-d cases via Lasso under specific sparsity and penalty conditions.
(2008).Honest variable selection in linear and logistic regression models via l1 andl 1+l2 penalization.Electronic Journal of Statistics.2, 1153–1194
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High Dimensional Gaussian and Bootstrap Approximations in Generalized Linear Models
Gaussian approximations hold for high-dimensional GLMs up to d = o(n^{2/5}) for convex sets while bootstrap approximations stay valid further, including in sparse exponential high-d cases via Lasso under specific sparsity and penalty conditions.