Quasi-Likelihood and/or Robust Estimation in High Dimensions
Statistics Theory
2013-01-07 v2 Methodology
Statistics Theory
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 -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 -penalized quasi-likelihood estimator has no false positives.
Cite
@article{arxiv.1206.6721,
title = {Quasi-Likelihood and/or Robust Estimation in High Dimensions},
author = {Sara van de Geer and Patric Müller},
journal= {arXiv preprint arXiv:1206.6721},
year = {2013}
}
Comments
Published in at http://dx.doi.org/10.1214/12-STS397 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org)