Convergence of generalized cross-validation for an ill-posed integral equation
Convergence of generalized cross-validation for an ill-posed integral equation
View/Date of Publication
12.2023Publisher
Institut für Numerische SimulationPublisher Location
BonnMetadata
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Citable Link (Handle URI) 
https://hdl.handle.net/20.500.11811/11571
Abstract
In this article we rigorously show consistency of generalized cross-validation applied to an exemplary ill-posed integral equation, given a finite number of noisy point evaluations. In particular, we present non-asymptotic order-optimal error estimates in probability. Hereby it is remarkable that the unknown true solution is not required to fulfill a self-similarity condition, which is generally needed for other heuristic parameter choice rules.
Subjects
statistical inverse problems, generalized cross-validation, consistency, error estimates
Classification (DDC)
510 Mathematik 518 Numerische AnalysisFirst Publication
https://ins.uni-bonn.de/publication/preprintsPart of Series
INS Preprints ; 2303Jahn, Tim: Convergence of generalized cross-validation for an ill-posed integral equation. In: INS Preprints, 2303.
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11571
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11571
@unpublished{handle:20.500.11811/11571,
author = {{Tim Jahn}},
title = {Convergence of generalized cross-validation for an ill-posed integral equation},
publisher = {Institut für Numerische Simulation},
year = 2023,
month = dec,
INS Preprints},
volume = 2303,
note = {In this article we rigorously show consistency of generalized cross-validation applied to an exemplary ill-posed integral equation, given a finite number of noisy point evaluations. In particular, we present non-asymptotic order-optimal error estimates in probability. Hereby it is remarkable that the unknown true solution is not required to fulfill a self-similarity condition, which is generally needed for other heuristic parameter choice rules.},
url = {https://hdl.handle.net/20.500.11811/11571}
}
author = {{Tim Jahn}},
title = {Convergence of generalized cross-validation for an ill-posed integral equation},
publisher = {Institut für Numerische Simulation},
year = 2023,
month = dec,
INS Preprints},
volume = 2303,
note = {In this article we rigorously show consistency of generalized cross-validation applied to an exemplary ill-posed integral equation, given a finite number of noisy point evaluations. In particular, we present non-asymptotic order-optimal error estimates in probability. Hereby it is remarkable that the unknown true solution is not required to fulfill a self-similarity condition, which is generally needed for other heuristic parameter choice rules.},
url = {https://hdl.handle.net/20.500.11811/11571}
}
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