Bauer, Benedikt ; Heimrich, Felix ; Kohler, Michael ; Krzyzak, Adam (2017)
On estimation of surrogate models for multivariate computer experiments.
In: Annals of the Institute of Statistical Mathematics, 69
Artikel, Bibliographie
Kurzbeschreibung (Abstract)
Estimation of surrogate models for computer experiments leads to nonparametric regression estimation problems without noise in the dependent variable. In this paper, we propose an empirical maximal deviation minimization principle to construct estimates in this context and analyze the rate of convergence of corresponding quantile estimates. As an application, we consider estimation of computer experiments with moderately high dimension by neural networks and show that here we can circumvent the so-called curse of dimensionality by imposing rather general assumptions on the structure of the regression function. The estimates are illustrated by applying them to simulated data and to a simulation model in mechanical engineering.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2017 |
| Autor(en): | Bauer, Benedikt ; Heimrich, Felix ; Kohler, Michael ; Krzyzak, Adam |
| Art des Eintrags: | Bibliographie |
| Titel: | On estimation of surrogate models for multivariate computer experiments |
| Sprache: | Englisch |
| Publikationsjahr: | 2 November 2017 |
| Verlag: | Springer |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Annals of the Institute of Statistical Mathematics |
| Jahrgang/Volume einer Zeitschrift: | 69 |
| URL / URN: | Http://10.1007/s10463-017-0627-8 |
| Kurzbeschreibung (Abstract): | Estimation of surrogate models for computer experiments leads to nonparametric regression estimation problems without noise in the dependent variable. In this paper, we propose an empirical maximal deviation minimization principle to construct estimates in this context and analyze the rate of convergence of corresponding quantile estimates. As an application, we consider estimation of computer experiments with moderately high dimension by neural networks and show that here we can circumvent the so-called curse of dimensionality by imposing rather general assumptions on the structure of the regression function. The estimates are illustrated by applying them to simulated data and to a simulation model in mechanical engineering. |
| Fachbereich(e)/-gebiet(e): | 16 Fachbereich Maschinenbau > Fachgebiet Datenverarbeitung in der Konstruktion (DiK) (ab 01.09.2022 umbenannt in "Product Life Cycle Management") 04 Fachbereich Mathematik 04 Fachbereich Mathematik > Stochastik DFG-Sonderforschungsbereiche (inkl. Transregio) > Sonderforschungsbereiche > SFB 805: Beherrschung von Unsicherheit in lasttragenden Systemen des Maschinenbaus DFG-Sonderforschungsbereiche (inkl. Transregio) > Sonderforschungsbereiche 16 Fachbereich Maschinenbau DFG-Sonderforschungsbereiche (inkl. Transregio) |
| Hinterlegungsdatum: | 04 Dez 2017 07:53 |
| Letzte Änderung: | 04 Dez 2017 07:53 |
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