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On estimation of surrogate models for multivariate computer experiments

Author

Listed:
  • Benedikt Bauer

    (Technische Universität Darmstadt)

  • Felix Heimrich

    (Technische Universität Darmstadt)

  • Michael Kohler

    (Technische Universität Darmstadt)

  • Adam Krzyżak

    (Concordia University)

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.

Suggested Citation

  • Benedikt Bauer & Felix Heimrich & Michael Kohler & Adam Krzyżak, 2019. "On estimation of surrogate models for multivariate computer experiments," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(1), pages 107-136, February.
    • Handle: RePEc:spr:aistmt:v:71:y:2019:i:1:d:10.1007_s10463-017-0627-8
    DOI: 10.1007/s10463-017-0627-8
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    References listed on IDEAS

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    1. Kohler, Michael & Krzyżak, Adam, 2013. "Optimal global rates of convergence for interpolation problems with random design," Statistics & Probability Letters, Elsevier, vol. 83(8), pages 1871-1879.
    2. Kohler, Michael, 2014. "Optimal global rates of convergence for noiseless regression estimation problems with adaptively chosen design," Journal of Multivariate Analysis, Elsevier, vol. 132(C), pages 197-208.
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    Cited by:

    1. Plassier, Vincent & Portier, François & Segers, Johan, 2020. "Risk bounds when learning infinitely many response functions by ordinary linear regression," LIDAM Discussion Papers ISBA 2020019, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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