Unbiased Estimators and Multilevel Monte Carlo

• 成果类型: Article
• 署名作者: Vihola, Matti
• 署名单位: University of Jyvaskyla
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2017.1670
• 发表日期: 2018
• 页码: 448-462
• 关键词: simulation

摘要

Multilevel Monte Carlo (MLMC) and recently proposed unbiased estimators are closely related. This connection is elaborated by presenting a new general class of unbiased estimators, which admits previous debiasing schemes as special cases. New lower variance estimators are proposed, which are stratified versions of earlier unbiased schemes. Under general conditions, essentially when MLMC admits the canonical square root Monte Carlo error rate, the proposed new schemes are shown to be asymptotically as efficient as MLMC, both in terms of variance and cost. The experiments demonstrate that the variance reduction provided by the new schemes can be substantial.