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High-dimensional regression with unknown variance (Q5965306)

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scientific article; zbMATH DE number 6549001

Language	Label	Description	Also known as
English	High-dimensional regression with unknown variance	scientific article; zbMATH DE number 6549001

Statements

scholarly article

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High-dimensional regression with unknown variance (English)

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Christophe Giraud

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Nicolas Verzelen

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Statistical Science

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publication date

3 March 2016

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full work available at URL

https://arxiv.org/abs/1109.5587

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https://projecteuclid.org/euclid.ss/1356098553

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zbMATH Keywords

linear regression

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high-dimension

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unknown variance

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describes a project that uses

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MaRDI profile type

MaRDI publication profile

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Estimating Linear Restrictions on Regression Coefficients for Multivariate Normal Distributions

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Comments on: \(\ell_{1}\)-penalization for mixture regression models

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A survey of cross-validation procedures for model selection

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Segmentation of the mean of heteroscedastic data via cross-validation

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A simple proof of the restricted isometry property for random matrices

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Estimator selection with respect to Hellinger-type risks

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Gaussian model selection with an unknown variance

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Estimator selection in the Gaussian setting

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Risk bounds for model selection via penalization

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Slope heuristics: overview and implementation

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Square-root lasso: pivotal recovery of sparse signals via conic programming

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Simultaneous analysis of Lasso and Dantzig selector

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Gaussian model selection

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Minimal penalties for Gaussian model selection

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Optimal selection of reduced rank estimators of high-dimensional matrices

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Aggregation for Gaussian regression

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The Dantzig selector: statistical estimation when \(p\) is much larger than \(n\). (With discussions and rejoinder).

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Atomic Decomposition by Basis Pursuit

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A new algorithm for fixed design regression and denoising

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The \(L_1\) convergence of kernel density estimates

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Observed universality of phase transitions in high-dimensional geometry, with implications for modern data analysis and signal processing

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Compressed sensing

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Least angle regression. (With discussion)

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Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties

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The Predictive Sample Reuse Method with Applications

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Sparsity regret bounds for individual sequences in online linear regression

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Mixing least-squares estimators when the variance is unknown

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Estimation of Gaussian graphs by model selection

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Low rank multivariate regression

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High-dimensional regression with unknown variance

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Graph Selection with GGMselect

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A transformation theorem for one-dimensional \(f\)-expansions

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Asymptotically optimal difference-based estimation of variance in nonparametric regression

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The benefit of group sparsity

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Robust Statistics

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Reduced-rank regression for the multivariate linear model

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UPS delivers optimal phase diagram in high-dimensional variable selection

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Rank penalized estimators for high-dimensional matrices

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Nuclear-norm penalization and optimal rates for noisy low-rank matrix completion

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Detecting multiple change-points in the mean of Gaussian process by model selection

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Information Theory and Mixing Least-Squares Regressions

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Asymptotic optimality for \(C_ p\), \(C_ L\), cross-validation and generalized cross-validation: Discrete index set

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Oracle inequalities and optimal inference under group sparsity

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Some Comments on C P

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High-dimensional graphs and variable selection with the Lasso

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Estimation of (near) low-rank matrices with noise and high-dimensional scaling

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Asymptotic properties of criteria for selection of variables in multiple regression

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The Bayesian Lasso

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Minimax Rates of Estimation for High-Dimensional Linear Regression Over $\ell_q$-Balls

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Exponential screening and optimal rates of sparse estimation

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Estimation of high-dimensional low-rank matrices

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Estimating the dimension of a model

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Linear Model Selection by Cross-Validation

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An optimal selection of regression variables

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\(\ell_{1}\)-penalization for mixture regression models

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Comments on: \(\ell _{1}\)-penalization for mixture regression models

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Sparsity and Smoothness Via the Fused Lasso

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On the conditions used to prove oracle results for the Lasso

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High-dimensional Gaussian model selection on a Gaussian design

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Minimax risks for sparse regressions: ultra-high dimensional phenomenons

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Information-Theoretic Limits on Sparsity Recovery in the High-Dimensional and Noisy Setting

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Model Selection and Estimation in Regression with Grouped Variables

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Nearly unbiased variable selection under minimax concave penalty

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Learning Bounds for Kernel Regression Using Effective Data Dimensionality

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Adaptive Forward-Backward Greedy Algorithm for Learning Sparse Representations

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The Adaptive Lasso and Its Oracle Properties

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Regularization and Variable Selection Via the Elastic Net

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Identifiers

zbMATH Open document ID

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10.1214/12-STS398

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:5965306

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