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

Matthias Hansmann (), Benjamin M. Horn (), Michael Kohler () and Stefan Ulbrich ()
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Matthias Hansmann: TU Darmstadt
Benjamin M. Horn: TU Darmstadt
Michael Kohler: TU Darmstadt
Stefan Ulbrich: TU Darmstadt

Metrika: International Journal for Theoretical and Applied Statistics, 2022, vol. 85, issue 3, No 3, 323-343

Abstract: 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.

Keywords: Conditional distribution function estimation; Consistency; Experimental fatigue tests; Local averaging estimate; Shape optimization; Isogeometric analysis; 62G05; 62G20 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s00184-021-00831-4

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