Statistical minimax approach of the Hausdorff moment problem

Details Statistical minimax approach of the Hausdorff moment problem Statistical minimax approach of the Hausdorff moment problem

2007-05-09

arxiv.org/abs/0705.1235v3

Mathematics

Statistics Theory

21 pages

Scientific paper

10.1088/0266-5611/24/4/045018

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.

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