Consistency of randomized integration methods
| Autor: | Hofstadler, Julian, Rudolf, Daniel |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.jco.2023.101740 |
| Popis: | We prove that a class of randomized integration methods, including averages based on $(t,d)$-sequences, Latin hypercube sampling, Frolov points as well as Cranley-Patterson rotations, consistently estimates expectations of integrable functions. Consistency here refers to convergence in mean and/or convergence in probability of the estimator to the integral of interest. Moreover, we suggest median modified methods and show for integrands in $L^p$ with $p>1$ consistency in terms of almost sure convergence Comment: 17 pages. Accepted for publication in Journal of Complexity |
| Databáze: | arXiv |
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