Statistical minimax approach of the Hausdorff moment problem
arXiv:0705.1235 · doi:10.1088/0266-5611/24/4/045018
Abstract
The purpose of this paper is to study the problem of estimating a compactly supported density of probability from noisy observations of its moments. In fact, we provide a statistical approach to the famous Hausdorff classical moment problem. We prove an upper bound and a lower bound on the rate of convergence of the mean squared error showing that the considered estimator attains minimax rate over the corresponding smoothness classes.
21 pages