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Minimax lower bounds are pessimistic in nature: for any given estimator, minimax lower bounds yield the existence of a worst-case target vector $\beta^*_{worst}$ for which the prediction error of the given estimator is bounded from below.
Assouad, fano, and le cam
Bin Yu · 1997
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Empirical minimization
Peter L Bartlett and Shahar Mendelson · 2006
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A simple proof of the restricted isometry property for random matrices
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Simultaneous analysis of lasso and dantzig selector
Peter J. Bickel, Ya’acov Ritov, and Alexandre B. Tsybakov · 2009
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Introduction to nonparametric estimation
Alexandre B. Tsybakov · 2009
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Restricted eigenvalue properties for correlated gaussian designs
Garvesh Raskutti, Martin J Wainwright, and Bin Yu · 2010
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Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization
Benjamin Recht, Maryam Fazel, and Pablo A Parrilo · 2010
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Statistics for high-dimensional data: methods, theory and applications
Peter Bühlmann and Sara Van De Geer · 2011
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Oracle inequalities and optimal inference under group sparsity
Karim Lounici, Massimiliano Pontil, Sara van de Geer, and Alexandre B. Tsybakov · 2011
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Optimal upper and lower bounds for the true and empirical excess risks in heteroscedastic least-squares regression
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Stéphane Boucheron, Gábor Lugosi, and Pascal Massart · 2013
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Reconstruction from anisotropic random measurements
Mark Rudelson and Shuheng Zhou · 2013
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A new perspective on least squares under convex constraint
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On concentration for (regularized) empirical risk minimization
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Optimal prediction for sparse linear models? lower bounds for coordinate-separable m-estimators
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Slope meets lasso: improved oracle bounds and optimality
Pierre C Bellec, Guillaume Lecué, and Alexandre B Tsybakov · 2016
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Slope is adaptive to unknown sparsity and asymptotically minimax
Weijie Su and Emmanuel Candes · 2016
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Introduction to high-dimensional statistics , volume 138
Christophe Giraud · 2014
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Concentration behavior of the penalized least squares estimator
Alan Muro and Sara van de Geer · 2015
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Probability theory: The coupling method
Frank den Hollander
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Bounds on the prediction error of penalized least squares estimators with convex penalty
Pierre C Bellec and Alexandre B Tsybakov · 2017
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A note on the approximate admissibility of regularized estimators in the gaussian sequence model
Xi Chen, Adityanand Guntuboyina, and Yuchen Zhang · 2017
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On the prediction performance of the lasso
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