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Nonparametric quantile estimation using surrogate models and importance sampling

Author

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  • Michael Kohler

    (Technische Universität Darmstadt)

  • Reinhard Tent

    (Technische Universität Darmstadt)

Abstract

Given a costly to compute function $$m: {\mathbb {R}}^d\rightarrow {\mathbb {R}}$$m:Rd→R, which is part of a simulation model, and an $${\mathbb {R}}^d$$Rd-valued random variable with known distribution, the problem of estimating a quantile $$q_{m(X),\alpha }$$qm(X),α is investigated. The presented approach has a nonparametric nature. Monte Carlo quantile estimates are obtained by estimating m through some estimate (surrogate) $$m_n$$mn and then by using an initial quantile estimate together with importance sampling to construct an importance sampling surrogate quantile estimate. A general error bound on the error of this quantile estimate is derived, which depends on the local error of the function estimate $$m_n$$mn, and the convergence rates of the corresponding importance sampling surrogate quantile estimates are analyzed. The finite sample size behavior of the estimates is investigated by applying the estimates to simulated data.

Suggested Citation

  • Michael Kohler & Reinhard Tent, 2020. "Nonparametric quantile estimation using surrogate models and importance sampling," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(2), pages 141-169, February.
    • Handle: RePEc:spr:metrik:v:83:y:2020:i:2:d:10.1007_s00184-019-00736-3
    DOI: 10.1007/s00184-019-00736-3
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    References listed on IDEAS

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    1. Neddermeyer, Jan C., 2009. "Computationally Efficient Nonparametric Importance Sampling," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 788-802.
    2. Michael Kohler & Adam Krzyżak & Reinhard Tent & Harro Walk, 2018. "Nonparametric quantile estimation using importance sampling," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(2), pages 439-465, April.
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