Second-order Stein: SURE for SURE and other applications in high-dimensional inference
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Publication:2054467
DOI10.1214/20-AOS2005zbMath1486.62209arXiv1811.04121OpenAlexW3204172662MaRDI QIDQ2054467
Publication date: 3 December 2021
Published in: The Annals of Statistics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1811.04121
model selectionregressionvariance estimateelastic netStein's formularisk estimatedebiased estimationSURE for SUREvariance of model size
Multivariate distribution of statistics (62H10) Estimation in multivariate analysis (62H12) Ridge regression; shrinkage estimators (Lasso) (62J07) Robustness and adaptive procedures (parametric inference) (62F35) Nonparametric tolerance and confidence regions (62G15)
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Cites Work
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- On asymptotically optimal confidence regions and tests for high-dimensional models
- Nearly unbiased variable selection under minimax concave penalty
- Statistical significance in high-dimensional linear models
- Kullback-Leibler aggregation and misspecified generalized linear models
- Degrees of freedom in lasso problems
- Statistics for high-dimensional data. Methods, theory and applications.
- Deviation optimal learning using greedy \(Q\)-aggregation
- The sparsity and bias of the LASSO selection in high-dimensional linear regression
- Estimation of the mean of a multivariate normal distribution
- Ordered linear smoothers
- Bounds on the prediction error of penalized least squares estimators with convex penalty
- Optimal bounds for aggregation of affine estimators
- Regularization and the small-ball method. I: Sparse recovery
- Honest confidence regions for nonparametric regression
- Adaptive estimation of a quadratic functional by model selection.
- Weak convergence and empirical processes. With applications to statistics
- Sharp oracle inequalities for aggregation of affine estimators
- The Lasso problem and uniqueness
- Slope meets Lasso: improved oracle bounds and optimality
- Debiasing the Lasso: optimal sample size for Gaussian designs
- Pivotal estimation via square-root lasso in nonparametric regression
- Simultaneous analysis of Lasso and Dantzig selector
- Confidence sets in sparse regression
- Aggregation of affine estimators
- High-dimensional graphs and variable selection with the Lasso
- Concentration Inequalities
- Sparse Matrix Inversion with Scaled Lasso
- Confidence Intervals and Hypothesis Testing for High-Dimensional Regression
- Newton-Stein Method: An optimization method for GLMs via Stein's Lemma
- Adapting to Unknown Smoothness via Wavelet Shrinkage
- Scaled sparse linear regression
- Just relax: convex programming methods for identifying sparse signals in noise
- Information Theory and Mixing Least-Squares Regressions
- Normal Approximation by Stein’s Method
- Unbiased Risk Estimates for Singular Value Thresholding and Spectral Estimators
- A short survey of Stein's method
- Inference on Treatment Effects after Selection among High-Dimensional Controls
- The degrees of freedom of the Lasso for general design matrix
- Analysis and Geometry of Markov Diffusion Operators
- Sharp Thresholds for High-Dimensional and Noisy Sparsity Recovery Using $\ell _{1}$-Constrained Quadratic Programming (Lasso)
- Excess Optimism: How Biased is the Apparent Error of an Estimator Tuned by SURE?
- Some Comments on C P
- Confidence Intervals for Low Dimensional Parameters in High Dimensional Linear Models
- Mean Field Models for Spin Glasses
- Convex functions and their applications. A contemporary approach
- High-dimensional regression with unknown variance
- Sparse estimation by exponential weighting
- A general theory of concave regularization for high-dimensional sparse estimation problems
