  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.
