Nonparametric quantile estimation using surrogate models and importance sampling

Michael Kohler () and Reinhard Tent ()
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Michael Kohler: Technische Universität Darmstadt
Reinhard Tent: Technische Universität Darmstadt

Metrika: International Journal for Theoretical and Applied Statistics, 2020, vol. 83, issue 2, No 1, 169 pages

Abstract: 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.

Keywords: Nonparametric quantile estimation; Importance sampling; Surrogate models; Rate of convergence; Primary 62G05; Secondary 62G30 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s00184-019-00736-3

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