A deconvolution path for mixtures

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.

References in corpus (4)

• Bayes and empirical-Bayes multiplicity adjustment in the variable-selection problem
• General maximum likelihood empirical Bayes estimation of normal means
• Posterior concentration rates for empirical Bayes procedures, with applications to Dirichlet Process mixtures
• Nonparametric density estimation by histogram trend filtering