Minimax goodness-of-fit testing in ill-posed inverse problems with partially unknown operators

DOI10.1214/16-AIHP768zbMath1384.62151arXiv1503.08562OpenAlexW2963402842MaRDI QIDQ1700386

Clément Marteau, Theofanis Sapatinas

Publication date: 5 March 2018

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1503.08562

zbMATH Keywords

singular value decompositionellipsoidscompact operatorsGaussian white noise modelill-posed inverse problemsGaussian sequence modelminimax signal detectionminimax goodness-of-fit testing

Mathematics Subject Classification ID

Nonparametric hypothesis testing (62G10) Asymptotic properties of nonparametric inference (62G20) Nonparametric estimation (62G05)

Related Items (3)

Deep learning for inverse problems with unknown operator ⋮ Adaptive minimax testing for circular convolution ⋮ Rate optimal estimation of quadratic functionals in inverse problems with partially unknown operator and application to testing problems

Cites Work

• Unnamed Item
• Risk hull method and regularization by projections of ill-posed inverse problems
• Minimax signal detection in ill-posed inverse problems
• A unified treatment for non-asymptotic and asymptotic approaches to minimax signal detection
• Deconvolution problems in nonparametric statistics
• A deconvolution approach to estimation of a common shape in a shifted curves model
• Adaptive estimation of a quadratic functional by model selection.
• Oracle inequalities for inverse problems
• Sharp adaptation for inverse problems with random noise
• Nonparametric goodness-of-fit testing under Gaussian models
• Penalized blockwise Stein's method, monotone oracles and sharp adaptive estimation
• Non-asymptotic minimax rates of testing in signal detection
• Non asymptotic minimax rates of testing in signal detection with heterogeneous variances
• Blockwise SVD with error in the operator and application to blind deconvolution
• Minimax nonparametric testing in a problem related to the Radon transform
• Fréchet means of curves for signal averaging and application to ECG data analysis
• Goodness-of-fit testing and quadratic functional estimation from indirect observations
• Nonlinear estimation for linear inverse problems with error in the operator
• Testing for Lack of Fit in Inverse Regression—with Applications to Biophotonic Imaging
• Adaptive Gaussian Inverse Regression with Partially Unknown Operator
• An alternative point of view on Lepski's method
• Testing a Parametric Model Against a Nonparametric Alternative with Identification Through Instrumental Variables
• Adaptive estimation for inverse problems with noisy operators

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