Nonparametric quantile estimation using surrogate models and importance sampling
| Autor: | Michael Kohler, Reinhard Tent |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
Statistics::Theory 05 social sciences Monte Carlo method Nonparametric statistics Function (mathematics) 01 natural sciences 010104 statistics & probability Distribution (mathematics) Sample size determination 0502 economics and business Statistics::Methodology Applied mathematics 0101 mathematics Statistics Probability and Uncertainty Random variable Importance sampling 050205 econometrics Mathematics Quantile |
| Zdroj: | Metrika. 83:141-169 |
| ISSN: | 1435-926X 0026-1335 |
| DOI: | 10.1007/s00184-019-00736-3 |
| Popis: | Given a costly to compute function $$m: {\mathbb {R}}^d\rightarrow {\mathbb {R}}$$, which is part of a simulation model, and an $${\mathbb {R}}^d$$-valued random variable with known distribution, the problem of estimating a quantile $$q_{m(X),\alpha }$$ is investigated. The presented approach has a nonparametric nature. Monte Carlo quantile estimates are obtained by estimating m through some estimate (surrogate) $$m_n$$ 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 $$m_n$$, 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. |
| Databáze: | OpenAIRE |
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