  The task of mixture proportion estimation (MPE) is to estimate the weight of
a component distribution in a mixture, given observations from both the
component and mixture. Previous work on MPE adopts the irreducibility
assumption, which ensures identifiablity of the mixture proportion. In this
paper, we propose a more general sufficient condition that accommodates several
settings of interest where irreducibility does not hold. We further present a
resampling-based meta-algorithm that takes any existing MPE algorithm designed
to work under irreducibility and adapts it to work under our more general
condition. Our approach empirically exhibits improved estimation performance
relative to baseline methods and to a recently proposed regrouping-based
algorithm.
