When is the optimal regularization parameter insensitive to the choice of the loss function?

DOI10.1080/03610929008830285zbMath0724.62044OpenAlexW2024602863WikidataQ63508141 ScholiaQ63508141MaRDI QIDQ3212129

Yonghua Wang, Grace Wahba

Publication date: 1990

Published in: Communications in Statistics - Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03610929008830285

zbMATH Keywords

convergence ratesFredholm integral equationdeconvolutionmean square errorgeneralized cross-validationpenalty functionaloptimal smoothing parameteroptimal regularization parameterfirst kind integral equations with noisy data

Mathematics Subject Classification ID

Density estimation (62G07) Numerical methods for integral equations (65R20) Nonparametric inference (62G99)

Related Items (15)

Asymptotic optimality of generalized cross-validation for choosing the regularization parameter ⋮ Probabilistic regularization of Fredholm integral equations of the first kind ⋮ A generalized correlated \(C_p\) criterion for derivative estimation with dependent errors ⋮ Performance of Robust GCV and Modified GCV for Spline Smoothing ⋮ On average case complexity of linear problems with noisy information ⋮ On a numerical technique regarding inversion of the Laplace transform ⋮ Unnamed Item ⋮ Small area estimation under a spatially non-linear model ⋮ Estimation of the Regularization Parameter in Linear Discrete Ill-Posed Problems Using the Picard Parameter ⋮ A note on wavelet estimation of the derivatives of a regression function in a random design setting ⋮ Comparing parameter choice methods for regularization of ill-posed problems ⋮ Unnamed Item ⋮ Smoothed Nonparametric Derivative Estimation Based on Weighted Difference Sequences ⋮ Parameter Choices for Fast Harmonic Spline Approximation ⋮ Gradient-based smoothing parameter selection for nonparametric regression estimation

Cites Work

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• Error bounds for derivative estimates based on spline smoothing of exact or noisy data
• 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
• Convergence rates for regularized solutions of integral equations from discrete noisy data
• Smoothing noisy data with spline functions: Estimating the correct degree of smoothing by the method of generalized cross-validation
• Improved estimates of statistical regularization parameters in Fourier differentiation and smoothing
• Cross-Validated Spline Methods for the Estimation of Three-Dimensional Tumor Size Distributions from Observations on Two-Dimensional Cross Sections
• Convergence Rates for Regularized Solutions

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