Optimal rate estimation of the mixing distribution in Poisson mixture models via Laplace inversion
Chris A. J. Klaassen, Robert M. Mnatsakanov · UvA-DARE (University of Amsterdam) · 2020
Consistent estimators of the mixing distribution in Poisson mixture models are constructed for both the right censored and the uncensored case. The estimators are based on a kind of Laplace inversion via factorial moments. The rate of convergence of the mean integrated squared error of these estimators is (log n/ log log n) 2. It is also shown that there do not exist estimators for which this rate is better.