6533b86efe1ef96bd12cbf96
RESEARCH PRODUCT
Unbiased Estimators and Multilevel Monte Carlo
Matti Viholasubject
FOS: Computer and information sciencesMonte Carlo methodWord error rate010103 numerical & computational mathematicsstochastic differential equationManagement Science and Operations ResearchStatistics - Computation01 natural sciences010104 statistics & probabilityStochastic differential equationstratificationSquare rootFOS: MathematicsApplied mathematics0101 mathematicsComputation (stat.CO)stokastiset prosessitMathematicsProbability (math.PR)ta111EstimatorVariance (accounting)unbiased estimatorsComputer Science ApplicationsMonte Carlo -menetelmät65C05 (Primary) 65C30 (Secondary)efficiencykerrostuneisuusVariance reductionunbiasemultilevel Monte CarlodifferentiaaliyhtälötMathematics - Probabilitydescription
Multilevel Monte Carlo (MLMC) and unbiased estimators recently proposed by McLeish (Monte Carlo Methods Appl., 2011) and Rhee and Glynn (Oper. Res., 2015) 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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2018-01-01 | Operations Research |