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
Article, Bibliographie
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.
| Item Type: | Article |
|---|---|
| Erschienen: | 2017 |
| Creators: | Bauer, Benedikt ; Heimrich, Felix ; Kohler, Michael ; Krzyzak, Adam |
| Type of entry: | Bibliographie |
| Title: | On estimation of surrogate models for multivariate computer experiments |
| Language: | English |
| Date: | 2 November 2017 |
| Publisher: | Springer |
| Journal or Publication Title: | Annals of the Institute of Statistical Mathematics |
| Volume of the journal: | 69 |
| URL / URN: | Http://10.1007/s10463-017-0627-8 |
| 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. |
| Divisions: | 16 Department of Mechanical Engineering > Department of Computer Integrated Design (DiK) (from 01.09.2022 renamed "Product Life Cycle Management") 04 Department of Mathematics 04 Department of Mathematics > Stochastik DFG-Collaborative Research Centres (incl. Transregio) > Collaborative Research Centres > CRC 805: Control of Uncertainty in Load-Carrying Structures in Mechanical Engineering DFG-Collaborative Research Centres (incl. Transregio) > Collaborative Research Centres 16 Department of Mechanical Engineering DFG-Collaborative Research Centres (incl. Transregio) |
| Date Deposited: | 04 Dec 2017 07:53 |
| Last Modified: | 04 Dec 2017 07:53 |
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