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


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. "Quasi-Likelihood and/or Robust Estimation in High Dimensions." Statist. Sci. 27 (4) 469 - 480, November 2012.


Published: November 2012
First available in Project Euclid: 21 December 2012

zbMATH: 1331.62354
MathSciNet: MR3025129
Digital Object Identifier: 10.1214/12-STS397

Keywords: high-dimensional model , Quasi-likelihood estimation , robust estimation , Sparsity , Variable selection

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.27 • No. 4 • November 2012
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