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
Article, Bibliographie
This is the latest version of this item.
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.
| Item Type: | Article |
|---|---|
| Erschienen: | 2022 |
| Creators: | Hansmann, Matthias ; Horn, Benjamin M. ; Kohler, Michael ; Ulbrich, Stefan |
| Type of entry: | Bibliographie |
| Title: | Estimation of conditional distribution functions from data with additional errors applied to shape optimization |
| Language: | English |
| Date: | April 2022 |
| Place of Publication: | Berlin ; Heidelberg |
| Publisher: | Springer |
| Journal or Publication Title: | Metrika |
| Volume of the journal: | 85 |
| Issue Number: | 3 |
| DOI: | 10.1007/s00184-021-00831-4 |
| Corresponding Links: | |
| 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. |
| Uncontrolled Keywords: | Conditional distribution function estimation, Consistency, Experimental fatigue tests, Local averaging estimate, Shape optimization, Isogeometric analysis |
| Additional Information: | Mathematics Subject Classification: 62G05, 62G20 |
| Classification DDC: | 500 Science and mathematics > 510 Mathematics |
| Divisions: | 04 Department of Mathematics 04 Department of Mathematics > Optimization 04 Department of Mathematics > Stochastik |
| Date Deposited: | 19 Mar 2024 10:10 |
| Last Modified: | 19 Mar 2024 10:10 |
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| Suche nach Titel in: | TUfind oder in Google |
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Estimation of conditional distribution functions from data with additional errors applied to shape optimization. (deposited 18 Mar 2024 13:50)
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