Efficient algorithms for robust generalized cross-validation spline smoothing

DOI10.1016/j.cam.2010.05.016zbMath1201.65024OpenAlexW2081084507MaRDI QIDQ711231

Mark A. Lukas, Frank R. de Hoog, Robert S. Anderssen

Publication date: 25 October 2010

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2010.05.016

zbMATH Keywords

algorithmstracesplineparameter selectionCholesky decompositiongeneralized cross-validationsmoothing parametersmoothing matrix

Mathematics Subject Classification ID

Nonparametric regression and quantile regression (62G08) Numerical computation using splines (65D07) Numerical smoothing, curve fitting (65D10)

Related Items

Concentration inequalities for cross-validation in scattered data approximation ⋮ Performance of Robust GCV and Modified GCV for Spline Smoothing ⋮ Differentiation of matrix functionals using triangular factorization ⋮ Practical use of robust GCV and modified GCV for spline smoothing ⋮ Fast cross-validation in harmonic approximation ⋮ Interpolating log-determinant and trace of the powers of matrix \(\mathbf{A}+ t\mathbf{B}\)

Uses Software

• gss

Cites Work

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• Smoothing by spline functions. II
• Linear smoothers and additive models
• Spline smoothing and optimal rates of convergence in nonparametric regression models
• An efficient method for calculating smoothing splines using orthogonal transformations
• A fast ``Monte-Carlo cross-validation procedure for large least squares problems with noisy data
• Smoothing noisy data with spline functions: Estimating the correct degree of smoothing by the method of generalized cross-validation
• Smoothing by spline functions.
• A general method for the construction of interpolating or smoothing spline-functions
• Performance of Robust GCV and Modified GCV for Spline Smoothing
• Differentiation of matrix functionals using triangular factorization
• An Algorithm for the Regularization of Ill-Conditioned, Banded Least Squares Problems
• Robust generalized cross-validation for choosing the regularization parameter
• A Stochastic Estimator of the Trace of the Influence Matrix for Laplacian Smoothing Splines
• Making robust the cross-validatory choice of smoothing parameter in spline smoothing regression
• Strong robust generalized cross-validation for choosing the regularization parameter
• A comparison of the Reinsch and Speckman splines
• Smoothing Spline Gaussian Regression: More Scalable Computation via Efficient Approximation
• Confidence Intervals for Nonparametric Curve Estimates
• Computation of Smoothing and Interpolating Natural Splines via Local Bases
• Smoothing noisy data with spline functions
• Smoothing spline ANOVA models