Convergence analysis of Tikhonov regularization for non-linear statistical inverse problems

DOI10.1214/20-EJS1735zbMath1473.65065arXiv1902.05404OpenAlexW3048309030MaRDI QIDQ2192321

Peter Mathé, Gilles Blanchard, Abhishake Rastogi

Publication date: 17 August 2020

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

Full work available at URL: https://arxiv.org/abs/1902.05404

zbMATH Keywords

Tikhonov regularizationreproducing kernel Hilbert spaceminimax convergence ratesstatistical inverse problemgeneral source condition

Mathematics Subject Classification ID

Nonparametric regression and quantile regression (62G08) Asymptotic properties of nonparametric inference (62G20) Numerical solutions to equations with nonlinear operators (65J15) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Numerical solution to inverse problems in abstract spaces (65J22) Nonlinear algebraic or transcendental equations (65Hxx)

Related Items (4)

Convergence Rates for Learning Linear Operators from Noisy Data ⋮ Convex regularization in statistical inverse learning problems ⋮ Inverse learning in Hilbert scales ⋮ Nonlinear Tikhonov regularization in Hilbert scales for inverse learning

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