Nonparametric quantile estimation using importance sampling |
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Authors: | Michael Kohler Adam Krzyżak Reinhard Tent Harro Walk |
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Institution: | 1.Fachbereich Mathematik,Technische Universit?t Darmstadt,Darmstadt,Germany;2.Department of Computer Science and Software Engineering,Concordia University,Montreal,Canada;3.Fachbereich Mathematik,Universit?t Stuttgart,Stuttgart,Germany |
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Abstract: | Nonparametric estimation of a quantile of a random variable m(X) is considered, 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 a given density. An importance sampling quantile estimate of m(X), which is based on a suitable estimate \(m_n\) of m, is defined, and it is shown that this estimate achieves a rate of convergence of order \(\log ^{1.5}(n)/n\). The finite sample size behavior of the estimate is illustrated by simulated data. |
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