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Recent Results on Nonparametric Quantile Estimation in a Simulation Model

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Challenges in Computational Statistics and Data Mining

Part of the book series: Studies in Computational Intelligence ((SCI,volume 605))

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Abstract

We present recent results on nonparametric estimation of a quantile of distribution of Y given by a simulation model \(Y=m(X)\), where \(m: \mathbb {R}^d\rightarrow \mathbb {R}\) is a function which is costly to compute and X is a \(\mathbb {R}^d\)-valued random variable with given density. We argue that importance sampling quantile estimate of m(X), based on a suitable estimate \(m_n\) of m achieves better rate of convergence than the estimate based on order statistics alone. Similar results are given for Robbins-Monro type recursive importance sampling and for quantile estimation based on surrogate model.

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Acknowledgments

The author would like to thank his co-authors and acknowledge the support from the Natural Sciences and Engineering Research Council of Canada.

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Authors and Affiliations

  1. Department of Computer Science and Software Engineering, Concordia University, 1455 De Maisonneuve Blvd. West, Montreal, QC, H3G 1M8, Canada

    Adam Krzyżak

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  1. Adam Krzyżak
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Correspondence to Adam Krzyżak .

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Editors and Affiliations

  1. Faculty of Computer Science, Dalhousie University, Halifax, Nova Scotia, Canada

    Stan Matwin

  2. Institute of Computer Science, Polish Academy of Sciences, Warsaw, Poland, and Warsaw University of Technology, Warsaw, Poland

    Jan Mielniczuk

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Krzyżak, A. (2016). Recent Results on Nonparametric Quantile Estimation in a Simulation Model. In: Matwin, S., Mielniczuk, J. (eds) Challenges in Computational Statistics and Data Mining. Studies in Computational Intelligence, vol 605. Springer, Cham. https://doi.org/10.1007/978-3-319-18781-5_13

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  • DOI: https://doi.org/10.1007/978-3-319-18781-5_13

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  • Online ISBN: 978-3-319-18781-5

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