Performance of Robust GCV and Modified GCV for Spline Smoothing

DOI10.1111/j.1467-9469.2011.00736.xzbMath1246.62110OpenAlexW1936137514MaRDI QIDQ2911706

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

Publication date: 1 September 2012

Published in: Scandinavian Journal of Statistics (Search for Journal in Brave)

Full work available at URL: http://researchrepository.murdoch.edu.au/id/eprint/7336/

zbMATH Keywords

asymptoticnonparametric regressiongeneralized cross-validationsmall samplesSobolev error

Mathematics Subject Classification ID

Nonparametric regression and quantile regression (62G08) Asymptotic properties of nonparametric inference (62G20) Linear regression; mixed models (62J05)

Related Items

Robust GCV choice of the regularization parameter for correlated data ⋮ A parameter choice rule for Tikhonov regularization based on predictive risk ⋮ A method for choosing the smoothing parameter in a semi-parametric model for detecting change-points in blood flow ⋮ Performance criteria and discrimination of extreme undersmoothing in nonparametric regression ⋮ Efficient algorithms for robust generalized cross-validation spline smoothing ⋮ Practical use of robust GCV and modified GCV for spline smoothing

Uses Software

• gss
• SemiPar

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Efficient algorithms for robust generalized cross-validation spline smoothing
• The average posterior variance of a smoothing spline and a consistent estimate of the average squared error
• Spline smoothing and optimal rates of convergence in nonparametric regression models
• A comparison of GCV and GML for choosing the smoothing parameter in the generalized spline smoothing problem
• Asymptotic optimality of \(C_ L\) and generalized cross-validation in ridge regression with application to spline smoothing
• Approximation of method of regularization estimators
• Smoothing noisy data with spline functions: Estimating the correct degree of smoothing by the method of generalized cross-validation
• Asymptotic optimality of generalized cross-validation for choosing the regularization parameter
• On the efficiency of selection criteria in spline regression
• Selection criteria for scatterplot smoothers
• Functional data analysis.
• Some results on Tchebycheffian spline functions and stochastic processes
• Error bounds for spline and L-spline interpolation
• When is the optimal regularization parameter insensitive to the choice of the loss function?
• Asymptotic properties of penalized spline estimators
• Robust generalized cross-validation for choosing the regularization parameter
• Making robust the cross-validatory choice of smoothing parameter in spline smoothing regression
• Strong robust generalized cross-validation for choosing the regularization parameter
• Reducing variability of crossvalidation for smoothing-parameter choice
• Multivariate Smoothing Spline Functions
• Semiparametric Regression
• Smoothers and theC_p, Generalized Maximum Likelihood, and Extended Exponential Criteria
• Smoothing Spline Gaussian Regression: More Scalable Computation via Efficient Approximation
• Confidence Intervals for Nonparametric Curve Estimates
• Some Comments on C P
• Smoothing spline ANOVA models