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Estimation of conditional distribution functions from data with additional errors applied to shape optimization

Hansmann, Matthias ; Horn, Benjamin M. ; Kohler, Michael ; Ulbrich, Stefan (2024)
Estimation of conditional distribution functions from data with additional errors applied to shape optimization.
In: Metrika, 2022, 85 (3)
doi: 10.26083/tuprints-00023448
Article, Secondary publication, Publisher's Version

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Item Type: Article
Type of entry: Secondary publication
Title: Estimation of conditional distribution functions from data with additional errors applied to shape optimization
Language: English
Date: 18 March 2024
Place of Publication: Darmstadt
Year of primary publication: April 2022
Place of primary publication: Berlin ; Heidelberg
Publisher: Springer
Journal or Publication Title: Metrika
Volume of the journal: 85
Issue Number: 3
DOI: 10.26083/tuprints-00023448
Corresponding Links:
Origin: Secondary publication DeepGreen
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
Status: Publisher's Version
URN: urn:nbn:de:tuda-tuprints-234485
Additional Information:

Mathematics Subject Classification: 62G05, 62G20

Classification DDC: 500 Science and mathematics > 510 Mathematics
Divisions: 04 Department of Mathematics > Optimization
04 Department of Mathematics > Stochastik
Date Deposited: 18 Mar 2024 13:50
Last Modified: 30 Apr 2024 07:13
SWORD Depositor: Deep Green
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/23448
PPN: 517332817
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