  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.
