Minimax optimal estimators for general additive functional estimation

Olivier Collier (1, 2, 3) , Laëtitia Comminges (4, 3)

1 UPN - Université Paris Nanterre
2 MODAL'X - Modélisation aléatoire de Paris X
3 CREST - Centre de Recherche en Économie et Statistique
4 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

In this paper, we observe a sparse mean vector through Gaussian noise and we aim at estimating some additive functional of the mean in the minimax sense. More precisely, we generalize the results of (Collier et al., 2017, 2019) to a very large class of functionals. The optimal minimax rate is shown to depend on the polynomial approximation rate of the marginal functional, and optimal estimators achieving this rate are built.

Mots clés: Minimax estimation; additive functional; sparsity; polynomial approximation

Domaines: Théorie [stat.TH]

Olivier Collier, Laëtitia Comminges. Minimax optimal estimators for general additive functional estimation. 2019. ⟨hal-02273511⟩