Integration of bounded monotone functions: Revisiting the nonsequential case, with a focus on unbiased Monte Carlo (randomized) methods
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866913184884981760 |
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| author | Basak, Subhasish Bect, Julien Vazquez, Emmanuel |
| author_facet | Basak, Subhasish Bect, Julien Vazquez, Emmanuel |
| contents | In this article we revisit the problem of numerical integration for monotone bounded functions, with a focus on the class of nonsequential Monte Carlo methods. We first provide new a lower bound on the maximal $L^p$ error of nonsequential algorithms, improving upon a theorem of Novak when p > 1. Then we concentrate on the case p = 2 and study the maximal error of two unbiased methods-namely, a method based on the control variate technique, and the stratified sampling method. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2203_00423 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Integration of bounded monotone functions: Revisiting the nonsequential case, with a focus on unbiased Monte Carlo (randomized) methods Basak, Subhasish Bect, Julien Vazquez, Emmanuel Numerical Analysis Statistics Theory In this article we revisit the problem of numerical integration for monotone bounded functions, with a focus on the class of nonsequential Monte Carlo methods. We first provide new a lower bound on the maximal $L^p$ error of nonsequential algorithms, improving upon a theorem of Novak when p > 1. Then we concentrate on the case p = 2 and study the maximal error of two unbiased methods-namely, a method based on the control variate technique, and the stratified sampling method. |
| title | Integration of bounded monotone functions: Revisiting the nonsequential case, with a focus on unbiased Monte Carlo (randomized) methods |
| topic | Numerical Analysis Statistics Theory |
| url | https://arxiv.org/abs/2203.00423 |