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On estimation of surrogate models for multivariate computer experiments

Bauer, Benedikt and Heimrich, Felix and Kohler, Michael and Krzyzak, Adam (2017):
On estimation of surrogate models for multivariate computer experiments.
In: Annals of the Institute of Statistical Mathematics, Springer, 69, ISSN 1572-9052,
[Online-Edition: Http://10.1007/s10463-017-0627-8],
[Article]

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 and Heimrich, Felix and Kohler, Michael and Krzyzak, Adam
Title: On estimation of surrogate models for multivariate computer experiments
Language: English
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.

Journal or Publication Title: Annals of the Institute of Statistical Mathematics
Volume: 69
Publisher: Springer
Divisions: 16 Department of Mechanical Engineering > Department of Computer Integrated Design (DiK)
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
Official URL: Http://10.1007/s10463-017-0627-8
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