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Estimating quantiles in imperfect simulation models using conditional density estimation

Author

Listed:
  • Michael Kohler

    (Technische Universität Darmstadt)

  • Adam Krzyżak

    (Concordia University)

Abstract

In this article, we consider the problem of estimating quantiles related to the outcome of experiments with a technical system given the distribution of the input together with an (imperfect) simulation model of the technical system and (few) data points from the technical system. The distribution of the outcome of the technical system is estimated in a regression model, where the distribution of the residuals is estimated on the basis of a conditional density estimate. It is shown how Monte Carlo can be used to estimate quantiles of the outcome of the technical system on the basis of the above estimates, and the rate of convergence of the quantile estimate is analyzed. Under suitable assumptions, it is shown that this rate of convergence is faster than the rate of convergence of standard estimates which ignore either the (imperfect) simulation model or the data from the technical system; hence, it is crucial to combine both kinds of information. The results are illustrated by applying the estimates to simulated and real data.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:aistmt:v:72:y:2020:i:1:d:10.1007_s10463-018-0683-8
    DOI: 10.1007/s10463-018-0683-8
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    References listed on IDEAS

    as
    1. 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.
    2. Ann-Kathrin Bott & Michael Kohler, 2016. "Adaptive Estimation of a Conditional Density," International Statistical Review, International Statistical Institute, vol. 84(2), pages 291-316, August.
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    4. Bauer, Benedikt & Devroye, Luc & Kohler, Michael & Krzyżak, Adam & Walk, Harro, 2017. "Nonparametric estimation of a function from noiseless observations at random points," Journal of Multivariate Analysis, Elsevier, vol. 160(C), pages 93-104.
    5. Michael Kohler & Adam Krzyżak & Shashidhar Mallapur & Roland Platz, 2018. "Uncertainty Quantification in Case of Imperfect Models: A Non‐Bayesian Approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 45(3), pages 729-752, September.
    6. 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.
    7. Jianqing Fan & Tsz Ho Yim, 2004. "A crossvalidation method for estimating conditional densities," Biometrika, Biometrika Trust, vol. 91(4), pages 819-834, December.
    8. Tina Felber & Michael Kohler & Adam Krzyżak, 2015. "Adaptive density estimation based on real and artificial data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(1), pages 1-18, March.
    9. Raymond K. W. Wong & Curtis B. Storlie & Thomas C. M. Lee, 2017. "A frequentist approach to computer model calibration," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(2), pages 635-648, March.
    10. Fan, Jianqing & Yao, Qiwei & Tong, Howell, 1996. "Estimation of conditional densities and sensitivity measures in nonlinear dynamical systems," LSE Research Online Documents on Economics 6704, London School of Economics and Political Science, LSE Library.
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