A deconvolution path for mixtures

TL;DR

This paper introduces an efficient two-step deconvolution method for mixture models that provides a full deconvolution path, enabling sensitivity analysis and outperforming benchmark methods in various scenarios.

Contribution

It presents a novel 'bin-and-smooth' estimator that is computationally efficient, statistically sound, and offers a full deconvolution path for mixture models.

Findings

Provides a full deconvolution path for mixture models.

Achieves state-of-the-art performance compared to benchmarks.

Enables sensitivity analysis with minimal effort.

Abstract

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.