Adaptive Gaussian Inverse Regression with Partially Unknown Operator

DOI10.1080/03610926.2012.731548zbMath1347.62056arXiv1204.1226OpenAlexW2049681635MaRDI QIDQ4929192

Jan Johannes, Maik Schwarz

Publication date: 13 June 2013

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

Full work available at URL: https://arxiv.org/abs/1204.1226

zbMATH Keywords

Sobolev spacesmodel selectionLepski's methodminimax theoryadaptive nonparametric estimationGaussian sequence space modelmildly and severely ill-posed inverse problems

Mathematics Subject Classification ID

Nonparametric regression and quantile regression (62G08) Nonparametric estimation (62G05) Minimax procedures in statistical decision theory (62C20)

Related Items (5)

Estimation of convolution in the model with noise ⋮ Deep learning for inverse problems with unknown operator ⋮ Minimax goodness-of-fit testing in ill-posed inverse problems with partially unknown operators ⋮ Rate optimal estimation of quadratic functionals in inverse problems with partially unknown operator and application to testing problems ⋮ Nonparametric intensity estimation from noisy observations of a Poisson process under unknown error distribution

Cites Work

• Unnamed Item
• Bandwidth selection in kernel density estimation: oracle inequalities and adaptive minimax optimality
• On the optimal rates of convergence for nonparametric deconvolution problems
• Speed of estimation in positron emission tomography and related inverse problems
• Risk bounds for model selection via penalization
• Oracle inequalities for inverse problems
• Nonparametric quasi-maximum likelihood estimation for Gaussian locally stationary processes
• Nonlinear estimation for linear inverse problems with error in the operator
• Optimal Discretization of Inverse Problems in Hilbert Scales. Regularization and Self-Regularization of Projection Methods
• On optimal solutions of the deconvolution problem
• Deconvolving kernel density estimators
• On the effect of estimating the error density in nonparametric deconvolution
• On inverse problems with unknown operators
• Statistical Inverse Estimation in Hilbert Scales
• Adaptive estimation for inverse problems with noisy operators

This page was built for publication: Adaptive Gaussian Inverse Regression with Partially Unknown Operator