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arXiv · 1206.6721

Quasi-Likelihood and/or Robust Estimation in High Dimensions

Sara van de Geer·Patric Müller
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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.

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Sara van de Geer, Patric Müller. 2013-01-04. Quasi-Likelihood and/or Robust Estimation in High Dimensions. https://doi.org/10.1214/12-sts397

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