Asymptotic optimality of generalized cross-validation for choosing the regularization parameter

DOI10.1007/BF01385687zbMath0791.65037OpenAlexW2139300206MaRDI QIDQ1326436

Mark A. Lukas

Publication date: 7 July 1994

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/133752

zbMATH Keywords

numerical differentiationregularization methodill-posed problemregularization parameterdata smoothingFourier differentiationmethod of generalized cross- validation

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Numerical solutions to equations with linear operators (65J10) Equations and inequalities involving linear operators, with vector unknowns (47A50) Numerical methods for ill-posed problems for integral equations (65R30) Numerical differentiation (65D25) Fredholm integral equations (45B05) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20)

Related Items (15)

Performance of Robust GCV and Modified GCV for Spline Smoothing ⋮ Adaptivity and Oracle Inequalities in Linear Statistical Inverse Problems: A (Numerical) Survey ⋮ A probabilistic oracle inequality and quantification of uncertainty of a modified discrepancy principle for statistical inverse problems ⋮ Empirical risk minimization as parameter choice rule for general linear regularization methods ⋮ Convergence rates for moment collocation solutions of linear operator equations ⋮ Robust GCV choice of the regularization parameter for correlated data ⋮ Hybrid regularisation and the (in)admissibility of ridge regression in infinite dimensional Hilbert spaces ⋮ On the discrepancy principle and generalised maximum likelihood for regularisation ⋮ Numerical differentiation of 2D functions from noisy data. ⋮ Heuristic Parameter Choice Rules for Tikhonov Regularization with Weakly Bounded Noise ⋮ Adaptive nonparametric instrumental variables estimation: empirical choice of the regularization parameter ⋮ A fast regularization parameter selection for regularly sampled 2D inputs ⋮ Performance criteria and discrimination of extreme undersmoothing in nonparametric regression ⋮ Comparing parameter choice methods for regularization of ill-posed problems ⋮ Parameter Choices for Fast Harmonic Spline Approximation

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