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We consider the problem of selecting the best estimator among a family of Tikhonov regularized estimators, or, alternatively, to select a linear combination of these regularizers that is as good as the best regularizer in the family.
Concentration of quadratic forms under a bernstein moment assumption
Pierre C. Bellec · 1901
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All admissible linear estimates of the mean vector
Arthur Cohen · 1966
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Some comments on c p
Colin L Mallows · 1973
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Generalized cross-validation as a method for choosing a good ridge parameter
Gene H Golub, Michael Heath, and Grace Wahba · 1979
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Asymptotic optimality of c _ l c\_l and generalized cross-validation in ridge regression with application to spline smoothing
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The Elements of Statistical Learning
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Complexity Theory: Quadratic Programming , pages 304–307
Stephen A. Vavasis · 2001
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Variance estimation in nonparametric regression via the difference sequence method
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Data-driven calibration of linear estimators with minimal penalties
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Stéphane Boucheron, Gábor Lugosi, and Pascal Massart · 2013
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Ordered smoothers with exponential weighting
Elena Chernousova, Yuri Golubev, Ekaterina Krymova, et al · 2013
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Hanson-wright inequality and sub-gaussian concentration
Mark Rudelson and Roman Vershynin · 2013
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Pivotal estimation via square-root lasso in nonparametric regression
Alexandre Belloni, Victor Chernozhukov, and Lie Wang · 2014
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Aggregation of affine estimators
D. Dai, P. Rigollet, Xia L., and Zhang T · 2014
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Aggregation and minimax optimality in high dimensional estimation
A.B. Tsybakov · 2014
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