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Integration of bounded monotone functions: Revisiting the nonsequential case, with a focus on unbiased Monte Carlo (randomized) methods

Abstract : 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.
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https://hal-centralesupelec.archives-ouvertes.fr/hal-03591555
Contributor : Julien Bect Connect in order to contact the contributor
Submitted on : Tuesday, June 14, 2022 - 3:22:38 PM
Last modification on : Monday, June 27, 2022 - 9:43:41 AM

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Distributed under a Creative Commons Attribution - NonCommercial - NoDerivatives 4.0 International License

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  • HAL Id : hal-03591555, version 2
  • ARXIV : 2203.00423

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Subhasish Basak, Julien Bect, Emmanuel Vazquez. Integration of bounded monotone functions: Revisiting the nonsequential case, with a focus on unbiased Monte Carlo (randomized) methods. 53èmes Journées de Statistique de la SFdS, Jun 2022, Lyon, France. ⟨hal-03591555v2⟩

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