Hansmann, Matthias ; Horn, Benjamin M. ; Kohler, Michael ; Ulbrich, Stefan (2022)
Estimation of conditional distribution functions from data with additional errors applied to shape optimization.
In: Metrika, 85 (3)
doi: 10.1007/s00184-021-00831-4
Artikel, Bibliographie
Dies ist die neueste Version dieses Eintrags.
Kurzbeschreibung (Abstract)
We study the problem of estimating conditional distribution functions from data containing additional errors. The only assumption on these errors is that a weighted sum of the absolute errors tends to zero with probability one for sample size tending to infinity. We prove sufficient conditions on the weights (e.g. fulfilled by kernel weights) of a local averaging estimate of the codf, based on data with errors, which ensure strong pointwise consistency. We show that two of the three sufficient conditions on the weights and a weaker version of the third one are also necessary for the spc. We also give sufficient conditions on the weights, which ensure a certain rate of convergence. As an application we estimate the codf of the number of cycles until failure based on data from experimental fatigue tests and use it as objective function in a shape optimization of a component.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2022 |
| Autor(en): | Hansmann, Matthias ; Horn, Benjamin M. ; Kohler, Michael ; Ulbrich, Stefan |
| Art des Eintrags: | Bibliographie |
| Titel: | Estimation of conditional distribution functions from data with additional errors applied to shape optimization |
| Sprache: | Englisch |
| Publikationsjahr: | April 2022 |
| Ort: | Berlin ; Heidelberg |
| Verlag: | Springer |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Metrika |
| Jahrgang/Volume einer Zeitschrift: | 85 |
| (Heft-)Nummer: | 3 |
| DOI: | 10.1007/s00184-021-00831-4 |
| Zugehörige Links: | |
| Kurzbeschreibung (Abstract): | We study the problem of estimating conditional distribution functions from data containing additional errors. The only assumption on these errors is that a weighted sum of the absolute errors tends to zero with probability one for sample size tending to infinity. We prove sufficient conditions on the weights (e.g. fulfilled by kernel weights) of a local averaging estimate of the codf, based on data with errors, which ensure strong pointwise consistency. We show that two of the three sufficient conditions on the weights and a weaker version of the third one are also necessary for the spc. We also give sufficient conditions on the weights, which ensure a certain rate of convergence. As an application we estimate the codf of the number of cycles until failure based on data from experimental fatigue tests and use it as objective function in a shape optimization of a component. |
| Freie Schlagworte: | Conditional distribution function estimation, Consistency, Experimental fatigue tests, Local averaging estimate, Shape optimization, Isogeometric analysis |
| Zusätzliche Informationen: | Mathematics Subject Classification: 62G05, 62G20 |
| Sachgruppe der Dewey Dezimalklassifikatin (DDC): | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
| Fachbereich(e)/-gebiet(e): | 04 Fachbereich Mathematik 04 Fachbereich Mathematik > Optimierung 04 Fachbereich Mathematik > Stochastik |
| Hinterlegungsdatum: | 19 Mär 2024 10:10 |
| Letzte Änderung: | 19 Mär 2024 10:10 |
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Estimation of conditional distribution functions from data with additional errors applied to shape optimization. (deposited 18 Mär 2024 13:50)
- Estimation of conditional distribution functions from data with additional errors applied to shape optimization. (deposited 19 Mär 2024 10:10) [Gegenwärtig angezeigt]
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