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Nonparametric estimation of a conditional density

Author

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  • Ann-Kathrin Bott

    (Technische Universität Darmstadt)

  • Michael Kohler

    (Technische Universität Darmstadt)

Abstract

In this paper, we estimate a conditional density. In contrast to standard results in the literature in this context we assume that for each observed value of the covariate we observe a sample of the corresponding conditional distribution of size larger than one. A density estimate is defined taking into account the data from all the samples by computing a weighted average using weights depending on the covariates. The error of the density estimate is measured by the $$L_1$$ L 1 -error. Results concerning consistency and rate of convergence of the estimate are presented, and the performance of the estimate for finite sample size is illustrated using simulated data. Furthermore, the estimate is applied to a problem in fatigue analysis.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:aistmt:v:69:y:2017:i:1:d:10.1007_s10463-015-0535-8
    DOI: 10.1007/s10463-015-0535-8
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    References listed on IDEAS

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    1. Jianqing Fan & Tsz Ho Yim, 2004. "A crossvalidation method for estimating conditional densities," Biometrika, Biometrika Trust, vol. 91(4), pages 819-834, December.
    2. 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.
    3. Jan G. De Gooijer & Dawit Zerom, 2003. "On Conditional Density Estimation," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 57(2), pages 159-176, May.
    4. Dmytro Furer & Michael Kohler, 2015. "Smoothing spline regression estimation based on real and artificial data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(6), pages 711-746, August.
    5. 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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    Cited by:

    1. 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.
    2. Matthias Hansmann & Benjamin M. Horn & Michael Kohler & Stefan Ulbrich, 2022. "Estimation of conditional distribution functions from data with additional errors applied to shape optimization," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(3), pages 323-343, April.

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