Statistical minimax approach of the Hausdorff moment problem

Thanh Mai Pham Ngoc (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

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.

Mots clés: Minimax estimation; Problem of the moments; Legendre polynomials; Kullback Leibler information; Density estimation

Domaines: Statistiques [math.ST]

Thanh Mai Pham Ngoc. Statistical minimax approach of the Hausdorff moment problem. 2007. ⟨hal-00145243v2⟩