Adaptive robust estimation in sparse vector model

DOI10.1214/20-AOS2002zbMath1476.62063arXiv1802.04230OpenAlexW3135175840MaRDI QIDQ820801

Laetitia Comminges, Mohamed Ndaoud, Olivier Collier, Alexandre B. Tsybakov

Publication date: 28 September 2021

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1802.04230

zbMATH Keywords

adaptive estimationrobust estimationfunctional estimationvariance estimationminimax ratesparse vector model

Mathematics Subject Classification ID

Functional data analysis (62R10) Nonparametric robustness (62G35) Linear regression; mixed models (62J05) Nonparametric estimation (62G05) Minimax procedures in statistical decision theory (62C20)

Related Items

All-in-one robust estimator of the Gaussian mean, On estimation of nonsmooth functionals of sparse normal means, Estimation of the \(\ell_2\)-norm and testing in sparse linear regression with unknown variance

Uses Software

• EigenPrism

Cites Work

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• Optimal rates of convergence for estimating the null density and proportion of nonnull effects in large-scale multiple testing
• Adaptive estimation of the sparsity in the Gaussian vector model
• Adaptive estimation of high-dimensional signal-to-noise ratios
• Minimax estimation of the noise level and of the deconvolution density in a semiparametric convolution model
• Robust covariance and scatter matrix estimation under Huber's contamination model
• Minimax risks for sparse regressions: ultra-high dimensional phenomenons
• Slope meets Lasso: improved oracle bounds and optimality
• Optimal adaptive estimation of linear functionals under sparsity
• Minimax estimation of linear and quadratic functionals on sparsity classes
• Minimax rate of testing in sparse linear regression
• Pivotal estimation via square-root lasso in nonparametric regression
• Noise level estimation in high-dimensional linear models
• Sparse covariance matrix estimation in high-dimensional deconvolution
• Scaled sparse linear regression
• Optimal Estimation of Genetic Relatedness in High-Dimensional Linear Models
• Pivotal Estimation in High-Dimensional Regression via Linear Programming
• EigenPrism: Inference for High Dimensional Signal-to-Noise Ratios
• Robust Statistics
• Introduction to nonparametric estimation