Abstract
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.
Citation
Sara van de Geer. Patric Müller. "Quasi-Likelihood and/or Robust Estimation in High Dimensions." Statist. Sci. 27 (4) 469 - 480, November 2012. https://doi.org/10.1214/12-STS397
Information