Convergence rates for regularized solutions of integral equations from discrete noisy data

DOI10.1214/aos/1176347125zbMath0672.62054OpenAlexW1964911840MaRDI QIDQ1120224

Douglas W. Nychka, Dennis D. Cox

Publication date: 1989

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aos/1176347125

zbMATH Keywords

convergence ratesstereologynonparametric regressionreproducing kernel spacemethod of regularizationAbel's equationestimation of particle size densitiesregularized histogram estimates

Mathematics Subject Classification ID

Linear regression; mixed models (62J05) Nonparametric estimation (62G05) Numerical methods for integral equations (65R20) Asymptotics of solutions to integral equations (45M05) (Semi-) Fredholm operators; index theories (47A53) Rate of convergence, degree of approximation (41A25)

Related Items

Asymptotic optimality of generalized cross-validation for choosing the regularization parameter, Smoothing Spline Semiparametric Density Models, Pointwise convergence in probability of general smoothing splines, Poisson inverse problems, When is the optimal regularization parameter insensitive to the choice of the loss function?, Asymptotic minimax rates for abstract linear estimators, On the discrepancy principle and generalised maximum likelihood for regularisation, Theoretical aspects of ill-posed problems in statistics, Regularized collocation method for Fredholm integral equations of the first kind, DEMAND ANALYSIS AS AN ILL-POSED INVERSE PROBLEM WITH SEMIPARAMETRIC SPECIFICATION, A new method of solving noisy Abel-type equations, Log-density estimation in linear inverse problems, Some comments on Wicksell's problem, Optimal indirect estimation for linear inverse problems with discretely sampled functional data, Spatially adaptive splines for statistical linear inverse problems