On the discrepancy principle and generalised maximum likelihood for regularisation

DOI10.1017/S0004972700014891zbMath0840.65043OpenAlexW2099886549MaRDI QIDQ4866745

Mark A. Lukas

Publication date: 18 March 1996

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0004972700014891

zbMATH Keywords

discrepancy principlegeneralized maximum likelihood

Mathematics Subject Classification ID

Nonparametric estimation (62G05) Numerical solutions to equations with linear operators (65J10) Numerical methods for ill-posed problems for integral equations (65R30) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20)

Related Items (4)

Adaptivity and Oracle Inequalities in Linear Statistical Inverse Problems: A (Numerical) Survey ⋮ Empirical risk minimization as parameter choice rule for general linear regularization methods ⋮ Comparing parameter choice methods for regularization of ill-posed problems ⋮ Parameter Choices for Fast Harmonic Spline Approximation

Cites Work

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• Asymptotic optimality of generalized cross-validation for choosing the regularization parameter
• Improved estimates of statistical regularization parameters in Fourier differentiation and smoothing
• Some results on Tchebycheffian spline functions and stochastic processes
• Convergence rates of certain approximate solutions to Fredholm integral equations of the first kind
• Numerical differentiation procedures for non-exact data
• Optimisation in the regularisation ill-posed problems
• Convergence Rates for Regularized Solutions
• Assessing regularised solutions
• Practical Approximate Solutions to Linear Operator Equations When the Data are Noisy
• Smoothing noisy data with spline functions

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