Sharp oracle inequalities for aggregation of affine estimators
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Publication:1940775
DOI10.1214/12-AOS1038zbMath1257.62038arXiv1104.3969OpenAlexW3105953504MaRDI QIDQ1940775
Arnak S. Dalalyan, Joseph Salmon
Publication date: 7 March 2013
Published in: The Annals of Statistics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1104.3969
Nonparametric regression and quantile regression (62G08) Asymptotic properties of nonparametric inference (62G20) Inequalities; stochastic orderings (60E15) Nonparametric estimation (62G05) Minimax procedures in statistical decision theory (62C20)
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Cites Work
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- Estimator selection in the Gaussian setting
- Sparse regression learning by aggregation and Langevin Monte-Carlo
- Mirror averaging with sparsity priors
- Kullback-Leibler aggregation and misspecified generalized linear models
- Exponential screening and optimal rates of sparse estimation
- On universal oracle inequalities related to high-dimensional linear models
- Deviation optimal learning using greedy \(Q\)-aggregation
- Generalized mirror averaging and \(D\)-convex aggregation
- Linear and convex aggregation of density estimators
- Nonparametric denoising of signals with unknown local structure. I: Oracle inequalities
- Minimax risk over hyperrectangles, and implications
- Mixing least-squares estimators when the variance is unknown
- Universal pointwise selection rule in multivariate function estimation
- Minimax multiple shrinkage estimation
- Optimal filtering of square-integrable signals in Gaussian noise
- Risk bounds for model selection via penalization
- Ordered linear smoothers
- Heuristics of instability and stabilization in model selection
- Aggregating regression procedures to improve performance
- Adaptive wavelet estimation: A block thresholding and oracle inequality approach
- Combining different procedures for adaptive regression
- Functional aggregation for nonparametric regression.
- Oracle inequalities for inverse problems
- Sharp adaptation for inverse problems with random noise
- Penalized blockwise Stein's method, monotone oracles and sharp adaptive estimation
- Statistical learning theory and stochastic optimization. Ecole d'Eté de Probabilitiés de Saint-Flour XXXI -- 2001.
- Boosting a weak learning algorithm by majority
- Sharp oracle inequalities for aggregation of affine estimators
- PAC-Bayesian bounds for sparse regression estimation with exponential weights
- On the optimality of the aggregate with exponential weights for low temperatures
- Some PAC-Bayesian theorems
- Aggregation for Gaussian regression
- Adaptive Minimax Estimation over Sparse $\ell_q$-Hulls
- PAC-Bayesian Generalisation Error Bounds for Gaussian Process Classification
- Competing against the Best Nearest Neighbor Filter in Regression
- Adapting to Unknown Smoothness via Wavelet Shrinkage
- Nonparametric statistical inverse problems
- Information Theory and Mixing Least-Squares Regressions
- Ideal spatial adaptation by wavelet shrinkage
- Learning Theory and Kernel Machines
- Aggregation by Exponential Weighting and Sharp Oracle Inequalities
- Model Selection and Estimation in Regression with Grouped Variables
- Prediction, Learning, and Games
- A Review of Image Denoising Algorithms, with a New One
- Introduction to nonparametric estimation