Asymptotically efficient estimation in measurement error models

Inference on linear functionals of the latent distribution in measurement error models is considered. The issue about asymptotically efficient estimation by maximum likelihood in a convolution model with Laplace error distribution is settled in the affirmative: maximum likelihood estimators of certain linear functionals of the mixing distribution are \sqrt{n}-consistent, asymptotically normal and efficient. Asymptotic normality of a Studentized version of the maximum likelihood estimator allows to construct confidence intervals for linear functionals. Regarding maximum likelihood estimation of the mixing distribution as a data-driven choice of the a priori distribution on the mixing parameter in an empirical Bayes approach to the problem of estimating the single means, a sequence of estimators can be constructed such that it is asymptotically optimal in a decision-theoretic sense.