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This work gives a simultaneous analysis of both the ordinary least squares estimator and the ridge regression estimator in the random design setting under mild assumptions on the covariate/response distributions.
Application of ridge analysis to regression problems
A. E. Hoerl · 1962
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Optimal global rates of convergence for nonparametric regression
C. J. Stone · 1982
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Matrix Analysis
R. Horn and C. R. Johnson · 1985
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Matrix Perturbation Theory
G. W. Stewart and J.-G. Sun · 1990
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Theory of Point Estimation
E. L. Lehmann and G. Casella · 1998
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Minimax risk: Pinsker bound
M. Nussbaum · 1999
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Adaptive estimation of a quadratic functional by model selection
B. Laurent and P. Massart · 2000
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Statistical Learning Theory and Stochastic Optimization, Lectures on Probability and Statistics, Ecole d’Eté de Probabilitiés de Saint-Flour XXXI – 2001
O. Catoni · 2004
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A Distribution-Free Theory of Nonparametric Regression
L. Györfi, M. Kohler, A. Kryżak, and H. Walk · 2004
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Learning bounds for kernel regression using effective data dimensionality
T. Zhang · 2005
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Local Rademacher complexities and oracle inequalities in risk minimization
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Learning theory estimates via integral operators and their approximations
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Effective resistances, statistical leverage, and applications to linear equation solving, 2010
P. Drineas and M. W. Mahoney · 2010
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Faster least squares approximation
P. Drineas, M. W. Mahoney, S. Muthukrishnan, and T. Sarlós · 2010
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Robust linear least squares regression
J.-Y. Audibert and O. Catoni · 2011
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A tail inequality for quadratic forms of subgaussian random vectors, 2011
D. Hsu, S. M. Kakade, and T. Zhang · 2011
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Approximate nearest neighbors and the fast Johnson-Lindenstrauss transform
N. Ailon and B. Chazelle · 2009
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Optimal rates for regularized least squares regression
I. Steinwart, D. Hush, and C. Scovel · 2009
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Tail inequalities for sums of random matrices that depend on the intrinsic dimension
D. Hsu, S. M. Kakade, and T. Zhang · 2012
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Loss minimization and parameter estimation with heavy tails, 2013
D. Hsu and S. Sabato · 2013
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