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Unbiased Estimators and Multilevel Monte Carlo

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Bibliographische Detailangaben
Zeitschriftentitel: Operations Research
Personen und Körperschaften: Vihola, Matti
In: Operations Research, 66, 2018, 2, S. 448-462
Medientyp: E-Article
Sprache: Englisch
veröffentlicht:
Institute for Operations Research and the Management Sciences (INFORMS)
Schlagwörter:
author_facet Vihola, Matti
Vihola, Matti
author Vihola, Matti
spellingShingle Vihola, Matti
Operations Research
Unbiased Estimators and Multilevel Monte Carlo
Management Science and Operations Research
Computer Science Applications
author_sort vihola, matti
spelling Vihola, Matti 0030-364X 1526-5463 Institute for Operations Research and the Management Sciences (INFORMS) Management Science and Operations Research Computer Science Applications http://dx.doi.org/10.1287/opre.2017.1670 <jats:p>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.</jats:p> Unbiased Estimators and Multilevel Monte Carlo Operations Research
doi_str_mv 10.1287/opre.2017.1670
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title Unbiased Estimators and Multilevel Monte Carlo
title_unstemmed Unbiased Estimators and Multilevel Monte Carlo
title_full Unbiased Estimators and Multilevel Monte Carlo
title_fullStr Unbiased Estimators and Multilevel Monte Carlo
title_full_unstemmed Unbiased Estimators and Multilevel Monte Carlo
title_short Unbiased Estimators and Multilevel Monte Carlo
title_sort unbiased estimators and multilevel monte carlo
topic Management Science and Operations Research
Computer Science Applications
url http://dx.doi.org/10.1287/opre.2017.1670
publishDate 2018
physical 448-462
description <jats:p>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.</jats:p>
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author Vihola, Matti
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description <jats:p>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.</jats:p>
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spelling Vihola, Matti 0030-364X 1526-5463 Institute for Operations Research and the Management Sciences (INFORMS) Management Science and Operations Research Computer Science Applications http://dx.doi.org/10.1287/opre.2017.1670 <jats:p>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.</jats:p> Unbiased Estimators and Multilevel Monte Carlo Operations Research
spellingShingle Vihola, Matti, Operations Research, Unbiased Estimators and Multilevel Monte Carlo, Management Science and Operations Research, Computer Science Applications
title Unbiased Estimators and Multilevel Monte Carlo
title_full Unbiased Estimators and Multilevel Monte Carlo
title_fullStr Unbiased Estimators and Multilevel Monte Carlo
title_full_unstemmed Unbiased Estimators and Multilevel Monte Carlo
title_short Unbiased Estimators and Multilevel Monte Carlo
title_sort unbiased estimators and multilevel monte carlo
title_unstemmed Unbiased Estimators and Multilevel Monte Carlo
topic Management Science and Operations Research, Computer Science Applications
url http://dx.doi.org/10.1287/opre.2017.1670