  We propose a class of estimators for deconvolution in mixture models based on
a simple two-step "bin-and-smooth" procedure applied to histogram counts. The
method is both statistically and computationally efficient: by exploiting
recent advances in convex optimization, we are able to provide a full
deconvolution path that shows the estimate for the mixing distribution across a
range of plausible degrees of smoothness, at far less cost than a full Bayesian
analysis. This enables practitioners to conduct a sensitivity analysis with
minimal effort. This is especially important for applied data analysis, given
the ill-posed nature of the deconvolution problem. Our results establish the
favorable theoretical properties of our estimator and show that it offers
state-of-the-art performance when compared to benchmark methods across a range
of scenarios.
