A deconvolution path for mixtures

作者：Madrid Padilla Oscar Hernan^*; Poison Nicholas G; Scott James

来源：Electronic Journal of Statistics, 2018, 12(1): 1717-1751.

DOI：10.1214/18-EJS1430

• Deconvolution
• mixture models
• penalized likelihood
• empirical Bayes
• sensitivity analysis

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.

• 出版日期2018