The Efficiency of Density Deconvolution

TL;DR

This paper demonstrates that non-parametric density deconvolution with Gaussian noise is statistically equivalent to a low-dimensional parametric problem, providing a new perspective on its efficiency using classical maximum likelihood theory.

Contribution

It introduces a novel framework linking density deconvolution with Gaussian noise to parametric models, simplifying the analysis of its statistical efficiency.

Findings

Density deconvolution behaves like a low-dimensional parametric problem.

Maximum likelihood estimation is effective for density deconvolution with Gaussian noise.

Classical likelihood theory can be used to analyze deconvolution efficiency.

Abstract

The density deconvolution problem involves recovering a target density g from a sample that has been corrupted by noise. From the perspective of Le Cam's local asymptotic normality theory, we show that non-parametric density deconvolution with Gaussian noise behaves similarly to a low-dimensional parametric problem that can easily be solved by maximum likelihood. This framework allows us to give a simple account of the statistical efficiency of density deconvolution and to concisely describe the effect of Gaussian noise on our ability to estimate g, all while relying on classical maximum likelihood theory instead of the kernel estimators typically used to study density deconvolution.