  We consider the theory for the high-dimensional generalized linear model with
the Lasso. After a short review on theoretical results in literature, we
present an extension of the oracle results to the case of quasi-likelihood
loss. We prove bounds for the prediction error and $\ell_1$-error. The results
are derived under fourth moment conditions on the error distribution. The case
of robust loss is also given. We moreover show that under an irrepresentable
condition, the $\ell_1$-penalized quasi-likelihood estimator has no false
positives.
