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Estimation of a density in a simulation model

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  • Ann-Kathrin Bott
  • Tina Felber
  • Michael Kohler

Abstract

The problem of estimating density in a simulation model is considered. Given a value of an -valued random input parameter X , the value of a real-valued random variable is computed. Here is a function which measures the quality of a technical system with input X . It is assumed that X and Y have densities. Given a sample of , the task is to estimate the density of Y . In a first step we estimate m and the density of X . Using these estimators we compute in a second step an estimator of the density of Y . Results concerning the -consistency and the rate of convergence are proven and the finite sample behaviour of the estimators is illustrated by applying them to simulated and real data.

Suggested Citation

  • Ann-Kathrin Bott & Tina Felber & Michael Kohler, 2015. "Estimation of a density in a simulation model," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(3), pages 271-285, September.
    • Handle: RePEc:taf:gnstxx:v:27:y:2015:i:3:p:271-285
    DOI: 10.1080/10485252.2015.1049601
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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.
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    Cited by:

    1. Ann-Kathrin Bott & Michael Kohler, 2017. "Nonparametric estimation of a conditional density," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(1), pages 189-214, February.
    2. Michael Kohler & Adam Krzyżak, 2020. "Estimating quantiles in imperfect simulation models using conditional density estimation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(1), pages 123-155, February.
    3. Benedict Götz & Sebastian Kersting & Michael Kohler, 2021. "Estimation of an improved surrogate model in uncertainty quantification by neural networks," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(2), pages 249-281, April.

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