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Nonparametric quantile estimation using importance sampling

Author

Listed:
  • Michael Kohler

    (Technische Universität Darmstadt)

  • Adam Krzyżak

    (Concordia University)

  • Reinhard Tent

    (Technische Universität Darmstadt)

  • Harro Walk

    (Universität Stuttgart)

Abstract

Nonparametric estimation of a quantile of a random variable m(X) is considered, where $$m: \mathbb {R}^d\rightarrow \mathbb {R}$$ m : R d → R is a function which is costly to compute and X is a $$\mathbb {R}^d$$ R d -valued random variable with a given density. An importance sampling quantile estimate of m(X), which is based on a suitable estimate $$m_n$$ m n of m, is defined, and it is shown that this estimate achieves a rate of convergence of order $$\log ^{1.5}(n)/n$$ log 1.5 ( n ) / n . The finite sample size behavior of the estimate is illustrated by simulated data.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:aistmt:v:70:y:2018:i:2:d:10.1007_s10463-016-0595-4
    DOI: 10.1007/s10463-016-0595-4
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    References listed on IDEAS

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    1. Kohler, Michael & Krzyżak, Adam & Walk, Harro, 2014. "Nonparametric recursive quantile estimation," Statistics & Probability Letters, Elsevier, vol. 93(C), pages 102-107.
    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.
    3. Neddermeyer, Jan C., 2009. "Computationally Efficient Nonparametric Importance Sampling," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 788-802.
    4. Tony Lancaster & Sung Jae Jun, 2010. "Bayesian quantile regression methods," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(2), pages 287-307.
    5. Jeremy Oakley, 2004. "Estimating percentiles of uncertain computer code outputs," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 53(1), pages 83-93, January.
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    Cited by:

    1. 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.

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