Quasi-likelihood and/or robust estimation in high dimensions

DOI10.1214/12-STS397zbMath1331.62354arXiv1206.6721MaRDI QIDQ5965304

Patric Müller, Sara van de Geer

Publication date: 3 March 2016

Published in: Statistical Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1206.6721

zbMATH Keywords

quasi-likelihood estimationvariable selectionrobust estimationsparsityhigh-dimensional model

Mathematics Subject Classification ID

Ridge regression; shrinkage estimators (Lasso) (62J07) Generalized linear models (logistic models) (62J12)

Related Items

Predictive functional linear models with diverging number of semiparametric single-index interactions, High-dimensional robust regression with \(L_q\)-loss functions, Test of significance for high-dimensional longitudinal data, Finite-sample analysis of \(M\)-estimators using self-concordance, Adaptive robust variable selection, On asymptotically optimal confidence regions and tests for high-dimensional models, Introduction to the special issue on sparsity and regularization methods, Quasi-likelihood and/or robust estimation in high dimensions, Penalized robust estimators in sparse logistic regression, High dimensional generalized linear models for temporal dependent data

Uses Software

• glmnet

Cites Work

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• Statistics for high-dimensional data. Methods, theory and applications.
• The Dantzig selector and sparsity oracle inequalities
• \(\ell_{1}\)-penalization for mixture regression models
• Sparsity in penalized empirical risk minimization
• Least squares estimation with complexity penalties
• About the constants in Talagrand's concentration inequalities for empirical processes.
• On the conditions used to prove oracle results for the Lasso
• The adaptive and the thresholded Lasso for potentially misspecified models (and a lower bound for the Lasso)
• Robust regression through the Huber's criterion and adaptive lasso penalty
• Simultaneous analysis of Lasso and Dantzig selector
• High-dimensional generalized linear models and the lasso
• Sparsity oracle inequalities for the Lasso
• Sup-norm convergence rate and sign concentration property of Lasso and Dantzig estimators
• Aggregation for Gaussian regression
• High-dimensional graphs and variable selection with the Lasso
• Classifiers of support vector machine type with \(\ell_1\) complexity regularization
• Estimation for High-Dimensional Linear Mixed-Effects Models Using ℓ1-Penalization
• Robust principal component analysis?
• Adaptive estimation with soft thresholding penalties
• De-noising by soft-thresholding
• Accuracy Guarantees for <formula formulatype="inline"> <tex Notation="TeX">$\ell_1$</tex></formula>-Recovery
• Aggregation and Sparsity Via ℓ1 Penalized Least Squares
• Sparse Density Estimation with ℓ1 Penalties
• The Lasso, correlated design, and improved oracle inequalities
• Quasi-likelihood and/or robust estimation in high dimensions
• A unified framework for high-dimensional analysis of \(M\)-estimators with decomposable regularizers