Quasi-Likelihood and/or Robust Estimation in High Dimensions
Copyright policy )Quasi-Likelihood and/or Robust Estimation in High Dimensions
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.
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)
FOS: Computer and information sciences, Generalized linear models (logistic models), Ridge regression; shrinkage estimators (Lasso), sparsity, Mathematics - Statistics Theory, robust estimation, Statistics Theory (math.ST), quasi-likelihood estimation, Methodology (stat.ME), High-dimensional model, FOS: Mathematics, high-dimensional model, Statistics - Methodology, variable selection
FOS: Computer and information sciences, Generalized linear models (logistic models), Ridge regression; shrinkage estimators (Lasso), sparsity, Mathematics - Statistics Theory, robust estimation, Statistics Theory (math.ST), quasi-likelihood estimation, Methodology (stat.ME), High-dimensional model, FOS: Mathematics, high-dimensional model, Statistics - Methodology, variable selection
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