Integration of bounded monotone functions: Revisiting the nonsequential case, with a focus on unbiased Monte Carlo (randomized) methods
Numerical Analysis
2024-01-05 v2 Numerical Analysis
Statistics Theory
Statistics Theory
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 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.
Keywords
Cite
@article{arxiv.2203.00423,
title = {Integration of bounded monotone functions: Revisiting the nonsequential case, with a focus on unbiased Monte Carlo (randomized) methods},
author = {Subhasish Basak and Julien Bect and Emmanuel Vazquez},
journal= {arXiv preprint arXiv:2203.00423},
year = {2024}
}