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The taut string approach to statistical inverse problems: theory and applications

Kim, Sangjin; Pokojovy, Michael; Wan, Xiang

Abstract:
A novel solution approach to a class of nonlinear statistical inverse problems with finitely many observations collected over a compact interval on the real line blurred by Gaussian white noise of arbitrary intensity is presented. Exploiting the nonparametric taut string estimator, we prove the state recovery strategy is convergent to a solution of the unnoisy problem at the rate of $n^{−1/2}$ as the number of observations n grows to infinity. Illustrations of the method's application to real-world examples from hydrology, civil & electrical engineering are given andan empirical study on the robustness of our approach is presented.

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Volltext §
DOI: 10.5445/IR/1000122342
Veröffentlicht am 04.08.2020
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsdatum 10.07.2020
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000122342
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 27 S.
Serie CRC 1173 Preprint ; 2020/19
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Externe Relationen Siehe auch
Schlagwörter inverse problems, signal processing, nonparametric statistics, taut string estimator, white noise
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