Minimax optimal estimators for general additive functional estimation

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...

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Bibliographic Details
Published inarXiv.org
Main Authors Collier, Olivier, Comminges, Laëtitia
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 29.08.2019
Subjects
Estimators
Minimax technique
Polynomials
Random noise
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Summary: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.
ISSN:2331-8422