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Minimax optimal estimators for general additive functional estimation

Collier, Olivier; Comminges, Laëtitia (2019-08), Minimax optimal estimators for general additive functional estimation. https://basepub.dauphine.fr/handle/123456789/20105

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Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-02273511
Date
2019-08
Publisher
Cahier de recherche CEREMADE, Université Paris-Dauphine
Series title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Published in
Paris
Pages
19
Metadata
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Author(s)
Collier, Olivier
Modélisation aléatoire de Paris X [MODAL'X]
Comminges, Laëtitia
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
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.
Subjects / Keywords
Minimax estimation; additive functional; sparsity; polynomial approximation