Nonparametric quantile estimation using importance sampling

Michael Kohler (), Adam Krzyżak (), Reinhard Tent () and Harro Walk ()
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Michael Kohler: Technische Universität Darmstadt
Adam Krzyżak: Concordia University
Reinhard Tent: Technische Universität Darmstadt
Harro Walk: Universität Stuttgart

Annals of the Institute of Statistical Mathematics, 2018, vol. 70, issue 2, No 12, 439-465

Abstract: 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.

Keywords: Nonparametric quantile estimation; Importance sampling; Rate of convergence (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10463-016-0595-4

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